 For the invitation. This is work which has been going on for quite a few years Those are my collaborators. The ones in red are postdocs are looking for permanent positions So if you see their names at when you have postdoc applications David Thornton used to be in red, but two weeks ago he got a Fellowship so he moved to the black part, but those guys are still in the market So you know when you have money and you want to get postdocs, you know go for them This is all the places which have given us money It's quite a few people and quite a few places So I'll begin very fast because most of you know a bit about about string theory So more than 20 years ago Stromiger and Wafa did a very nice calculation They looked in string theory in a regime of parameters where black holes don't exist gravity is zero But some system which has some charges Has the right properties to become a black hole when gravity is turned on and the system of strings and brains They just took the strings and brains and they completed their entropy and they found them They found a certain entropy and then they said okay less turn on gravity and when you turn on gravity The system of strings and brains actually becomes a black hole and then the entropy of this the entropy of the system of strings and brains Matches the entropy of the black hole. So this is a very nice Calculation and again, it's not it's not a calculation Which is just you know matching, you know five equals to five numbers equals to numbers This is really like you know hyper geometric functions and like you know modular forms equal modular forms You do two calculations in two very different parts of physics and you get the same answer It's clearly something something Shocking and amazing if you if you think about it So this entropy matching again is one of the big successes of string theory and again they have been about 2,000 papers Writing continuations of this on this work Now there's a no there's a more subtle question that you can ask which has to do more with what do We're discussing yesterday and you know the theme of this worship and the information paradox, which is okay great I have a nice calculation of the entropy of a statistical ensemble, but I can ask a more refined question What's happening if I take one particular microstate in this ensemble? I don't care about the ensemble I don't care about about Ensembles I just want one particular microstate of this in this ensemble and I want to understand what's happening When you increase the coupling and you go when it turn on gravity when you make gravity finite And the standard law has been again for many years following work by saskin Horace Pochinsky's kitty ball and the Gabriele Veneziano The standard law has been that you know this configuration of strings and brains when you turn on gravity Brains become smaller gravity is an attractive force. Why not gravity makes things smaller The horizon on the other hand grows with gravity So the horizon becomes bigger there's a correspondence point and then you recover the standard black holes So there's an expectation that you know the system each and every particular microstate to strum and rev up Accounted when you go to strong coupling to find a gravity becomes something which she knew which looks like a black hole has a horizon And you know it's basically distinguishable from a black hole outside of the horizon However over the past, you know almost 12 years has been 12 years It's hard to hard to fathom. We have discovered that some of the stormage of alpha microstates Not all of them not the typical one just some of them They have no intention of developing a horizon rather than when you go to the black hole regime of parameters They become something like this they become some geometries which have the same asymptotics as the black hole They have the same throat as the black hole But instead of having a horizon they have a smooth cap and each and every microstate Which you consider goes into a configuration which again looks like a black hole asymptotically But doesn't have a horizon instead. It has a smooth cap and the question Which one can ask again given by given the existence of these solutions and you know I have quite a few of these solutions by now the question is which one can ask is is it possible? That all the black or microstates all the microstates of the black hole which give which contribute to the entropy They actually look like this they are this kind of microstates which are again horizon as configurations and the black hole Therefore would be thought of not as a fundamental description of the of the physics But rather is a coarse-grain approximation and the real description of the physics is given by these microstates In a sense and this is again This was first put forth by mature it goes under the name of possible proposal But again it has many it has many other name it has many other names But in a sense what it implies if you think about an ideal gas if you think about an ideal gas And they want to make an analogy when you have an ideal gas you can describe the ideal gas in two ways You can describe it using fluid mechanics, you know PV equals an RT just treat the gas as a continuous fluid If you want to fly airplanes, you know You don't care too much about the fact that there is made of molecules and so on and so forth You just need to know some some heat capacities So you can describe there as an ideal as a fluid and you know It works very well however if you want to do short noise experiments if you want to do You know if you want to look at you know the at the universe that you know have a very very dilute plasmas you know that the air is not made of Continuous fluid air is made of molecules zooming around this room at you know 270 kilometers an hour and that's a real composition of the air So even if fluid mechanics is very good and you know again if you want to ventilate yourself You know use fluid mechanics don't care about the molecules The understanding that the air is really made of molecules and again you have many many states So again there in this room can be many states who are right now in a typical state Hopefully now, but you know the air can go very well in the corner and then all the molecules can go to the corner of that room And you know we can all die it can happen Okay, it's a very it's a very small chance for this to happen But you know it can happen so but we know that this is this is what this is what the room is made of It's made of this kind of molecules and What we're trying to argue is that the black hole in a similar fashion the black hole solution The one you find in nice beautiful in the GR textbooks the one which again you get you read in the You read in the textbooks the black hole solution is basically going to be a thermodynamic Description of the physics fluid mechanical description of the physics which is very good If you want to do gravitational lensing and you know far away behavior And you know if you want to understand the physics far away from the horizon It's a it's a perfect description again You know much like fluid mechanics is very good for flying airplanes But if you want to do near-horizon physics if you want to do if you want to understand for example information loss You cannot use fluid mechanics You have to use this new description in terms of microstate geometries And if you want to address for example information loss and maybe even gravity waves you have to actually Physics which happens very near the horizon you actually have to use this description Now it's very possible that the scale where fluid so then the question is you know One of the questions would be you know where does Fluid mechanics break down so you know you know when you have the air when you go to the scale of the mean free path Fluid mechanics breaks down the question is you know does fluid mechanic break down at the horizon or further out or maybe breaks Maybe the horizon is still is still captured by fluid mechanics. So this is this is really the big this is really the big The big question so now the question is there are some other ways of thinking about this this What we're trying to say so if this is true again if the black hole microstates are given by these geometries then in a sense We can say that the effective the effective field theory describing the black hole breaks down at the horizon There will be new physics coming out there and there's no space time inside black holes again This is another way to say what to rephrase what I'm saying inside black holes You don't have actual space time you have a you have a superposition of geometries Which does not look which does not have which does not which does not crystallize into space time So that's basically another way of seeing it There's another way if you know about ADS CFT many of you are holographists and you know many of you do ADS CFT and you know No ADS CFT better than you know They're more handy with ADS CFT than you know other other than other things in ADS CFT You have the boundary theory which has some states and there's an ensemble description of the states Strom and Jovapha match the ensemble with the black hole They say that basically every you know the entropy here is given by the entropy here What we're trying to show is that each and every one of one of the states in the boundary is due to some horizon as configurations And therefore the black hole is again the thermodynamic description of these horizon as configurations Now the water on to emphasis is this is this is not some hand-waving idea This is not this is something which one can really establish by like you know hardcore Calculations in string theory. This is not you know something which okay I like it you know is beautiful and you know let's say it's true This is something which you can really do you really have to do a lot of hardcore calculations in string theory To show to show that it's true Now a word of caution Ever since Hawking came up with the information paradox many many people have tried to say let's solve the information paradox By replacing the black hole by something a black or soliton or a gravity star or you know people want to have you know Firewalls nowadays and start hovering around above the horizon You know people in look quantum gravity even they have some pair of diagrams involving some look quantum gravity stuff Which again sits which actually sits again at the horizon scale There are many many people who are trying to replace the black hole by something this would be a very simple solution They are very simple solution to the information paradox it to solve the information paradox in five seconds but the problem is again as So yesterday it's easy this is very difficult It's very difficult to do that and if you want to do that you have to satisfy three very stringent tests and that's something which Gary Horowitz explained to me and you know I think it's it's one of the it's one one of the very deep things about about this stuff first of all If you want to replace the black hole horizon by something You have to the something you are using has to have the same growth with G Newton as the black hole horizon Why am I saying that if you look at the black hole size and you imagine making a Duncan experiment by which you increase G Newton your god You're playing with the constants of the universe and you increase G Newton you make G Newton stronger Then the gravity then the black hole horizon becomes bigger This is the only thing in the universe which becomes bigger when gravity in our universe When gravity becomes stronger normally gravity becoming stronger, you know tends to collapse things You know gravity is an attractive force you may gravity stronger your truck more you make things smaller So whatever you are replacing the black hole with has to grow with G Newton with the same With and and exactly the same rate as as the black hole horizon and that's something again very Very hard then you know if you just again build your favorite theory of quarks and you know Grava stars and stuff like that Whatever you build is going to become smaller with G Newton now with the black hole microstates I'm going to explain you I'm going to tell you about they do grow with G Newton And there's a very nice mechanism having to do with that with the fact that you are using to build them You're using deep brains deep brains are in a sense half solitonic objects They have a tension which grows which goes like one over G string and the deep brain because it's a solitonic object It actually becomes lighter when G Newton becomes bigger and because the deep brains become lighter there are some centrifugal forces and Given some angular momentum or configuration of deep brains because the deep brain is lighter. It actually becomes bigger So the ingredients which we are using again to replace the black hole Involve deep brains involved solitons involves objects which have tension which goes like one over G string And this is actually what makes these guys Able to replace the horizon otherwise again if you just you want to use normal matter you cannot do it This is test number one there's number two and that you have to have a mechanism to Not to foreign to the black hole and that's very difficult as As Was explained us yesterday if you want to put something again imagine the panel the panel's diagram I'm just having a cut of the panel's diagram. This is the black hole This is the inner horizon. This is out of horizon. You want to put some stuff You want to put some structure you want to put some garbage living here, but there's a problem Again, there's a GR dogma that the horizon should not put anything at the horizon and the reason is very simple The horizon is a null surface if you want to put something there you have to go the speed of light If whatever you're putting there is massive if it involves, you know anything massive any any any particles or anything It just falls in massive stuff doesn't want to go the speed of light just wants to go like this So it will fall into the black hole immediately So the black hole horizon really flushes inside it anything which one to try to put there naively if it's a massless object Then you can solve the wave equation in the black hole solution again It's a it's a textbook as a size is all the wave equation you find that whatever way profile you put there The black hole is going to eat it up very fast in a crossing time. It's gone So whatever massless profile you want to put there it dilutes very fast and you know it's gone So you cannot put stuff there You cannot just say oh I'm putting something at the horizon and I'm trying the black hole entropy This doesn't work. The horizon is null. You cannot have stuff leaving there No membrane no spins if you say I'm explaining the black the black hole entropy by putting a spin at the horizon up and down as As I was saying yesterday, you know, okay It's a nice picture and so on and so forth but these pins you know they are made of something and they just fall in whatever you want to put there whatever your your Favorite theory wants to put that the horizon is going to fall in and again same goes for the firewall Again, if you just say something must be there You have to find a support mechanism and that's something which is really really difficult thing and the reason is very Easy If you don't have a support and if you don't have a support mechanism This subject is going to fall in and most of the normal stuff is going to fall in if you don't have a support mechanism again It's really that you know, whatever you are doing. It's just it's just not it's just not right Number three is even worse If you think about gravitational collapse There's a lot of paper from Oppenheimer and Schneider back from 39 which considered the shell of dust coming in and forming a horizon So let's suppose you have a shell of dust which is you know huge which has the mass of the galaxy And the shell of dust is collapsing and at some point the shell of dust goes into the region Which is basically within its Schwarzschild radius and let's say this is the region here So I have a huge shell of dust No, this is supposed to be a shell of dust which has the mass of the galaxy of the saw of a huge size I'm letting it collapse at some point the shell of dust is collapsing and it's forming a horizon at That moment the curvature of space-time around the place of the horizon forms is very very small again If you take the black hole as which has the size of which has the size of the galaxy It's one of the things which don't didn't tell us yesterday You know when you cross the horizon of the black hole which has the size of the which has the Which is the one in the middle of the galaxy was the force you feel This is one of the skills of the black hole and you know don't didn't tell us yesterday How much is the tidal force but these forces are going to be very small You know, you can have if you make a mega big black hole the Tidal forces and the force which an observer feels when going through the horizon Whatever whatever she tidal forces they feel they're going to be smaller than gravity on the earth and gravity on the earth with trust We don't need to invoke you know quantum gravity and strings and so on and so forth So you expect that whenever the shell of dust is collapsing you're going to form very nicely a black hole You know, there's no problem You'll form a horizon and then you'll keep collapsing and you keep collapsing and you're collapsing and at some point The shell of dust is going to become very small very crumpled very strange There are going to be non perturbative effects deep rains and stuff like that and that's going to be here in this red region So you'll collapse the shell you'll form a horizon very happily and then at some point again You'll collapse, you know, you you'll have some stringy effects And you know, you know stuff is going to become high curvature and so on and so forth You'll have you have to throw it a theory and you have to invoke a new theory But then what you're trying to do you are trying to build something on the horizon You're trying to build some firewall You're trying to build some structure again at the on the horizon You have to convince this string red stuff here to give rise to this stuff here But as you see here, this is backwards in time So somehow if you have a shell of dust and you're collapsing it you're going to form stringy matter You have to go back one million years in time to form this structure at the scale of the horizon there's no and You know, so essentially by the time the shell becomes curved enough for for quantum effects to take it to become to become important The horizon and all the structure which could be the easy is in the causal path So this thing has to come out of out of out of nowhere and this cannot happen I mean again, you have to come you have to go back one million years backwards in time to create this structure So creating a structure the horizon is again Not very easy. How can you do it? How can you go backwards in time? The only mechanism to do that and again, this is one of the one of this This is one of one of the big counterarguments to whatever people want to do You know firewalls and fastballs whatever people want to do at the horizon The only way to convince this shell of dust To give rise to this structure is to actually make a tunnel And this is an argument very nice by by periklaus and samir matur Which then we make the very which actually we computed explicitly for some class of microset geometries If you look at the black hole The black hole has e to the s microstates and let's suppose the picture i'm telling you about is correct You are you know, let's let's suppose i'm able to build e to the s microset of the black hole Now the tunneling if i have a shell of dust the the shell of dust can tunnel into these microstates It's a very complicated process. I mean my microstate is a stringy thing So you know the shell of dust has to Go over a huge barrier But one can estimate the height of this barrier one can estimate how big is the tunneling probability And it's going to be heuristically over the e to the minus s That was the argument by klaus and matur and in the calculation we did involving some supersymmetric and near supersymmetric solutions We found it to actually be a slightly a slightly bit higher So then actually what's happening you have a shell of dust you have e to the minus e to the s Possible tunneling endpoints and the probability to tunnel into each and every one of them is e to the minus s And therefore when you have the shell of dust collapsing it will actually tunnel by the firm and golden rule with probability one So the shell of dust again if you have e to the s Horizon sized microstates by the time the shell of dust crosses a horizon It can tunnel into into all of them and the tunneling probability would be one and you'll not go here You'll form immediately one once you are here you'll tunnel and you'll form this structure This is the only way this is the only way to form this kind of Firewall fastball structure without going backwards in time. It has to be by tunneling So if you want to replace so if you want to replace The black hole horizon the black hole horizon by something You know if you want to build a structure there if you want to say, okay I'm building a structure is not enough to just give me one solution or two solutions or five solutions or 20 solutions You have to give me e to the s solutions You have to give me e to the s configurations Which are horizon sized if you don't give me this e to the s configurations if you only build, you know One or two or three solutions It this will not be enough this should I mean this doesn't mean that these solutions are going to be here You you'll not see the structure. You just have a horizon So again, the stakes are very high if you want to replace the black hole horizon by something You really have to do all these three things. You really have to build something which grows with gravity which Stays at the horizon and doesn't fall in and moreover It has a huge entropy that you have to build e to the s Of those things in order to argue that you can replace the horizon if you just build one of them Is not going to be enough So maybe it's a good place if people have questions. This is in a sense the motivation and this is the stakes of What we're doing Adding the criterion of being non-bps or very far from bps the same the same if you want to argue that Far from bps you have to find e to the s non-bps solutions. Yes. Yes. No, but I mean can you satisfy this? I'm coming. It's half of the talk is about is about that half of the talk is about supersymmetric half about about non supersymmetric, so If we consider a shell a collective shell in eight years Do you think that this mechanism should happen immediately after the formation of horizons or in particular that I think whatever Whatever theory you are having again if you have a black hole there should be to the s microstates if these microstates have horizon size this This can happen You know it's just it's it's it's moment. Okay the calculation we did about the tunneling and you know when we found so again This number this was estimated by crossing my tool using some black holes and using again some heuristic arguments But we had really microstates which we built and then we computed the tunneling probability really you know You have a brain going over some potential you really calculated this potential and we found this number a tiny bit more So somehow you are forming this you are forming this microstates a bit before forming the horizon We found that this number is not really to the minus s there's another big factor in front So you're actually tunneling a bit before the horizon forms Emission but it also works for tunneling So if I have e to the s possible endpoints and e to the minus s chance of going into one of them, then it's the full It's the transition probability. Yeah, it's not for me golden rule. Okay I'm sorry just to go back to my question. I think in ads there is some evidence that If you form a non-specific black hole by the collapse of the cell then at least Before the black hole gets very old The interior which is given by the source resolution I know But it depends on the tunneling again, you know, one would have to compare the tunneling so in ads I mean in the ads five But that's the whole point in the CFT calculation This is just thermalization and the question is, you know, when you thermalize What's the mechanism for thermalization? If I put a blob and and and so on and if you think about thermalization again I can ask what's the probability of tunneling between, you know, some some shell of quarglon plasma, which And you know the and the thermal things and if this is again It's a calculation. It's a calculation Which which one can do but you know, I think it can still be important I mean nobody has built these things in the bulk for for ads. Yes The Mathur picture assumes that all microstates are semi-classical. How? No, Mathur says there's something at the horizon And whatever something at the horizon is will have this entropy It doesn't say anything about semi-classical or not Semi-classical is what we are doing in SACLE and at USC with NIC because you know, those are the solutions We are building so right now we are doing semi-classical. I'll come at the end The question is whether this conclusion of calculation uses semi-classical Uses that all these things are semi-classical or not The Mathur calculation is very generic It's just saying when you have a black hole if you expect it to the e to the s solutions Which have black hole size which are just solutions of strength theory A concrete solution A concrete calculation So concrete calculation the one we have here is using semi-classical solutions The concrete calculation is using, you know, bubbling solutions which have like, you know, big bubbles and so on and so forth I need to keep it under under control So my calculation is really like, you know, classical solution with like, you know, go You know semi-classical solutions with like, you know, brainstorming and so on and so forth Mathur is saying something very generic He's just saying generically you expect the shell to be size to be the of the size of the black hole And, you know, the area the action is of this order and therefore this is of order e to the minus s But it could be, you know, if there's a factor of five here, it doesn't work You know, you need to compute the exact exponent I mean, if this kind of heuristic calculations of Krauss and Mathur, they are nice But, you know, in a real example, you have to compute the, you know, if the coefficient here is five And the coefficient here is one, this doesn't happen It's really, the exponents have to be the same And that's something which, again, it's hard to, you know, you cannot play with error bars in the exponent I mean, one has Okay, so now I'll tell you a bit how, a bit how we do this, how we build these solutions And in particular, both the supersymmetric and especially the non-supersymmetric, yes You would like to claim that semi-classical low-energy observers can distinguish all these individual e to the s Is that a statement you're going to make The tunneling of the, so the statement you're making is that when you have a shell of dust, it can tunnel into all of them Now, about observer, it's a different question. So about observer, I mean, I'll come towards the end The question is about a shell of dust. The question is when you form the black hole Because when you form the black hole, again, if you form the black hole Coming back here, if you form the black hole naively by collapsing a shell of dust And you don't have these tunneling effects You form a horizon And then by the time anything can happen, any, any, any strength you can take over, any quantum effects can become important You have to go back in time. You really have to go back in time to form this structure And that's something which now there's another question, which is, you know, secondary, which is, which Yan is asking What's happening if after forming this stuff There'll be an observer falling in and so on and so forth The observer can either hit this configuration or he can actually tunnel There's a big discussion about that. It has to do with possible complementarity So I think we'll have Some things to say about that. So there's a secondary question. What's happening when an observer goes through But for now, I mean, this is much more basic This is just a shell of dust collapsing and forming the black hole To form anything here, which is not a horizon, you have to tunnel, you have to tunnel Because otherwise, or, or you have to go back in time, in time a million years, you know, up to you Personally, I'd like to tunnel because again, I don't, you know I don't want quantum effects from a million years in the future to start affecting me now I mean, I just, you know, okay, maybe it can happen. Maybe quantum mechanics is crazy But, you know, I don't like that, you know, I just have my own My own biases and so on. But, you know, quantum mechanics from quantum effects from a million years in the future I don't like them at all That's, okay So the question, so, okay, let's give some examples So the first solution to look at again, if you're a strength theorist and you're constructing solutions We are looking for solutions which have a black hole size but no horizon The best is to use supersymmetric black holes and supersymmetric solutions is the easiest Because supersymmetric solutions are underlined by some linear system So, for example, if you take the black hole of stormage of alpha, the three charge black hole in five dimensions Um, this black hole can actually be replaced So you can actually argue that there's a solution Which has the same charges as the black hole and the same fluxes and this solution can be found in in in in in five-dimensional supergravity And the easiest is to look at so again the black hole is has a base is a solution which is built By taking some sources in an R4 base And you can find black hole microstates again horizonless configurations By replacing this R4 base by some four-dimensional hypercalor solution By some four-dimensional hypercalor base And in particular one can choose a four-dimensional base space Which is like this which is given by by Gibbons Hawking or by Tom Knott space So the black hole is given by a singularity in the horizon in R4 And the microstates come from replacing R4 by again by this hypercalor space And then building the solutions which are supersymmetric is not very hard On this hypercalor space you have to find a self-dual two form Which is again a straightforward calculation And then you have the black hole harmonic functions Which are given by this function z which are sourced by the magnetic two forms And then there's some electric magnetic interaction which gives you some rotation So usually when I have a pointing vector and have electric magnetic fields They give you some rotation So there's a system which one has to solve Again, you take a base space which is again, which you can take to be a Gibbons Hawking or a Tom Knott base space You solve the system of equations you eliminate singularities You eliminate closed time like curves and you find solutions which again do what you want And especially when you have this four-dimensional base space This Gibbons Hawking base space It was shown by Gauntlet-Gutowski and also by me and Perikraus in the corner That the solutions on this base space are given by eight harmonic functions What is the last equation you mean? This dk start dk So k is the one form the rotation one form. I haven't given in the metric The k is the rotation one form And dk is a two form and star dk is the is the horse-doll of that in four dimensions on the one the base space So this is the two form and this is the magnetic two form times the scalar work factors So this so these are scalars. These are just work factors And the g's are two forms So the last equation tells you that the rotation of the system Right hand side, what is this meaning the right hand side the right hand side You see you have some electric fields which are given by these z i's in the solution I'm not giving i'll show the solution a bit later You have some magnetic fields which are basically given by these g's And the the intuition behind the right hand side is that when you have an electric field and a magnetic field You have a pointing vector which gives you rotation So the rotation comes because you have electric magnetic fields which which have which are crossed That's the intuition behind this term But these terms are obtained by just solving supersymmetry variations in this particular space time So this so these equations are obtained, you know, quite painfully by solving supersymmetry variation I'm just giving you the finite the finite form So when you take a base space to be gibbons Hawking, it's very easy to it's very easy to construct solutions And in particular one can take a gibbon Hawking space which has many many centers Which are again, which can again have plus and minus signs between all these two centers. There's a there's a two form Okay, this is hard there's a if you look here You see when when the function v has a pole When the function v has a pole v to the minus one goes to zero So this fiber psi shrinks to zero at the pole of v So when v has many many poles you have a you have a u1 fiber or shrinks to zero at all these poles And therefore they are not trivial two cycles Between all these poles so between all these poles there are many many non trivial two cycles And one can actually construct solutions I'll tell you a bit later how these solutions come about one can construct solutions very easily Which have again many many two fluxes many many two cycles topological And they have fluxes wrapping this Wrapping these solutions and these solutions have the same mass and charge and angular momentum and the size as the black hole Now why do we have that? What's the what was the intuition behind the solutions? So again you have this you had a black hole before and i'm replacing the black hole By forming bubbles and by having magnetic flux wrapping the bubbles Now you can ask okay great. I have this configuration of bubbles and fluxes Why do why does it look does it look like a black hole? Where's the black hole charge coming from? To see the black hole charge is very easy. This is some five-dimensional super gravity Which have terms of the of the type f wedge f wedge a that's a term in the Lagrangian of five-dimensional super gravity And the charge is the coupling to a zero and when you have magnetic fluxes You see that in the Lagrangian there are terms which contain two magnetic fields sourcing a zero So your charge is sourced Not by singular objects not behind horizons when you have a black hole for example The charge comes from behind the horizon and you know the charge the flux line comes come outside From the from the horizon here the charge is sourced by basically having these magnetic fields You can ask where's the black hole mass coming from that's easy You know you have all the all these electrical magnetic fields They have energy and therefore they they give you the mass Whereas the angular momentum coming from it's coming from pointing vectors It's coming it's coming from e cross b and you see that when you have an a zero You have an f zero one for example, and then you have an f onto magnetic And therefore this is going to give you some angular momentum in the zero two direction So the angular momentum of these configurations Comes from basically fluxes talking to each other electric magnetic fluxes talking to each other That's the intuition. Of course, you know, I can you know, I can I can spend the whole hour explaining how these solutions are I mean, you know, this is quite a bit of work I'm just trying to give you a bit of a feeling if you have more questions and so on and on you know That's the solutions and the papers now these microstates actually they form black or solitons There's a funny story when I first came to france I gave a talk here tiboe and gary gibbons remember I gave a talk in i ts And I explained these solutions and you know, we had just found them and they were very happy And then tiboe and gary gibbons started grilling me and because you know I there are very simple to didn't understand about the solutions and so on and so forth and they're grilling me so much I remember exiting the room and you know walking through the i ts campus. I was like, oh my god Maybe these things are wrong. Maybe all these things which I've been doing over the past two or three years are just wrong I mean, I was so shaken by the all the questions. They asked me. I mean to just you know bombardment. I've never seen anything like that Uh, but then uh, and then you know gary kept on changing image with gary and then nick and gary They got together and they started to understand these things, you know, really from a hardcore Gr perspective, you know, you know more formal the way we had them was like, you know more like, you know, hand you know Hand waving America, you know west coast east coast, you know things and you know, they really got like a european frame of mind Okay, let's understand those things like you know thoroughly You know, let's get all the all the problems and the problem is those are black or solitones I mean the solutions if you if you think about them They are again they have black or charge and mass and angular momentum, but they have no horizon They're called black or solitones and there's a whole slew of theorems from like, you know 20 30 years ago forbidding black or soliton saying that black or should not exist in four dimensions and you know and all these theorems and you know basically Nick and gary. They basically found all the story behind them. You know why these solitones are allowed You know, what's the bug in these theorems is they There's a very very beautiful gr story behind them So, you know, if you want to if you really are a gary inclined person who likes, you know, who likes this kind of things You know, this is the place this is the place to read if you're a string theory more personal Okay, here's the brain here's another brain like me then, okay This is you know, this is this may be too formal for you, but you know for for hardcore people who like who like a gary understanding of this This is this is this is the paper and again, there isn't I mean I mean, you know, this I think I think the place where they started was you know in ihs, you know 10 years ago when when I gave when I came to france. Those of you who know about holography and klebanos thruster There's a similar system which appears again. This is just for the experts, you know There's in klebanos thruster. There's a charge in magnetic fluxes and again magnetic fluxes can carry can carry electric charge Now the difference between these solutions and the black hole is that the classical black hole solution has two scales It has the I mean on one hand you have the mass which gives you the horizon size and then you have the plank size These solutions are different these solutions. They stop the space time above the horizon So they have two more scales involved a normal black hole again has, you know, just two scales You know it has the mass and the plank length This solution is two more scales There's a scale where which tells you how far away from the horizon you are stopping the space time because again The solutions don't have a horizon so you know because you so so you are capping the space time above the horizon And there's something which which you can think about as as as the maximum redshift or the redshift from the bottom of the throat And this is something which you call z max And you know for a black hole the redshift is infinite, you know, you cannot put stuff there But on this solution you can you can put some you can put some stuff here And you can you can calculate, you know, what's the mass if I put, you know one one milligram of mass here And how much do you see at infinity and this is the maximum redshift So that's and that's a scale which these solutions have and the black hole doesn't have There's another scale which has to do with the size of the bubbles The only thing I told you is that I have topological cycles with flux But I haven't told you how big the cycles are the cycles could be one plank length each And you know they can have many many bubbles which are all one plank length each Or you can have like, you know one bubble which is, you know, mega big and huge And there are many and you know and then you can have everything in between And all these configurations again all these possibilities We can build solutions for all of them again Some of them are going to have more entropy some of them are going to have less entropy We don't know but this is a way to parameterize And roughly speaking the size of the bubble has to do with how much flux you put on it In a sense the flux blows up the bubble Because you have flux is the bubble the flux makes the bubble large So the more flux you put the bigger the bubble becomes the more the more the more magnetic flux You put on a two cycle the bigger the bubble becomes that's the intuition but again There are many calculations to to support them So this is nice and beautiful I mean again we have all these solutions You know which have you know which look like a black hole they have the same features But they don't have entropy they don't have too much entropy why the why don't they have entropy The reason is very stupid we started from a Gibbons Hawking space And you look for a solution the Gibbons Hawking isometry If you look at the molecules in this room which have an isometry You will grossly underestimate the entropy again But typical microstate of this room has molecules going around in all directions with all speeds If i'm looking only the molecule configuration which have some isometry Where the molecules go in a circle or something and I ask what's the entropy of those are grossly misestimate Are really underestimated entropy The most generic states should not have should not have isometries and again this solution which we build They are basically they have they have isometries Now the problem is in this game the balance is the following the more isometries you put the easier it is to build a solution If you put many isometries the solution is easy if you put few isometries the solution is hard But then if you want to get entropy You have to put you have to put few isometries So somehow the best is the hard the state of the art is to really find the balance between Finding solutions which are simple enough to be able to build and analyze and complicated enough to be able to get some entropy out of them That's somehow the balance. So one has to build more generic configurations There's a way to build them. There are some objects in string theory called super tubes Which actually can have arbitrary shape and still be super symmetric and to build these configurations We're able to put super tubes in these configurations. It's a top note space Don has found the greens functions for top notes for Scalers and vectors, you know, they're very painful. We use them to find these solutions It was a really painful piece of work and we got the super tubes and so on and so forth And they found it to be smooth and they found an entropy out of them I mean you can calculate how much entropy this super tube has and it comes like q to the five halves to the to the one quarter So it's really q to the five quarters Now that's a lot of entropy first of all should be highly impressed because I mean I'm getting e to the e to this number Worth of solutions. So that's a huge number of solutions which we are getting But it's not enough the black hole Q is the total charge. Yes, so the total so the entropy scales like q to the five quarters The black hole entropy the three charge black hole entropy scales like q to the three halves So this is not really black hole like so putting super tubes and doing you know page greens functions And you know all these calculations This is the first attempt ahead and it was not it was not enough And the reason was that in a sense the super tubes that you have here They are given by some functions which are arbitrary But somehow the number of functions determines how many degrees of freedom you have and you need to have So there's some when you come to want to calculate this number There's some cardi formula. There's a cardi formula and in the cardi formula when you put super tubes And you know you look at the entropy they have there's a center charge which is equal to eight for super tubes Now what we conjectured and and then okay, we said, okay, let's look for more generic things So then so yandabur and masaki shigemori and nika nai started to look look at more complicated string theory objects Which maybe have more degrees of freedom because again super tubes are not enough And they found this object which we call the super stratum Which is like a super tube. So this is a super tube. For example, imagine having a d1 and a d5 Brain, which is straight you can have these brains puffing up into a super tube And then they become functions of one variable But you can also have these brains wiggle in this direction by a momentum wave and then puff up And in general, there should be a more complicated configurations, which we call the super stratum Which should depend on function of two variables Now function of two variables are given by an infinite number of a function of two variables Is an infinite number of function of one variable if you just think about Fourier coefficients But of course, you know, when you have when you understand you have to quantize So you really have naively classically sequels to infinity But then you but then you know once you quantize you find that you know function of two variables You know there's a finite number of them So there's a finite number of degrees of freedom and this object to conjecture them to exist first of all and to be smooth And we are using this architectural version. There's some some tower in Katara, I think which is called the strata towers. So, you know, this is the architectural version Unfortunately building those things is quite hard. So this is what actually architecture people build So there's a difference between conception and you know implementation. Unfortunately for us, it was the same You know, it was very complicated to build the solutions But you know, we have been able to we have been able to build them But this is the kind of object which you expect you if you want to get black hole like entropy You need to have functions of two variables It's not enough to have it's not enough to have just super tubes and and so on you really have to do more Even more complicated stuff How did you build these objects? Well, if you think about a super tube, it's a just just again a circle in r4 But if you think about r4 as a gibbon-socking space Or if you think about top note, for example, a super tube is just something wrapping As an object which is wrapping the isometry direction of the gibbon-socking fiber, which is wrapping the top note fiber So this is really a top note space and the super tube is an object wrapping this top note fiber There's another direction in the game which is the direction of the d1 and the d5 brain again We're trying to get the stormage of alpha black hole which is d1 d5 and p charges There's a common d1 d5 direction which i'm calling here to be v And in our solutions, there's a solution for the super tube Where this v direction which is large at the location of the black of the d1 and the d5 Becomes zero at the location of the super tube And the side direction which is bigger the location of the super tube Becomes zero at the origin of the gibbon-socking space And you see that you have in the system a three sphere because again only have a u1 Which is bigger at one point as small as some other and another what u1 which is big at some point as small as some other this gives you a three sphere and The super strata which we are trying to build Again, there are some super tip solutions found ages ago by lunin and matura and by lunin and matura and maus Which depend on psi you can get solutions which depend on v pretty pretty easily And we're able to to build solutions which are parametrized by function of two variables by arbitrary functions f of psi and v And that's something which and then and that's something which We we did two years ago. Wow. Okay two years ago and because these paper have a more super stratum We are so happy that we found these things. I mean, you know after after quite after quite a while After several years of of trying it was it was a really painful process building the solutions again function of two variables now Why was it so hard for us when yan and masaki and nikon i can conjecture the super strata in 2011 and it took us, you know four years to find them now normally sakura. We tend to be a bit faster We have quite a few postdocs and you know, we usually do things much faster The problem is that if you look at these microsets of the black holes the black hole has three charges And they're all the microsets will should build they are building some u1 cube Supergravity in five dimensions again five dimension super gravities. There's a huge famine of them But we looked at one particular Truncation, which is a u1 cube supergravity and when we're trying to get wiggles on the supertubes we're getting singularities But then there was two there are two calculations one of them that done by Taylor and scandinavian carnation either using precision holography and the other one done by David Turton and Rodolfo and Stefan Augusto using string emission And these calculations told us that based on microscopic string theory calculations There should be another u1. There should be another u1 So even if the black hole only has three charges and you have three magnetic charges, there must be generically another Another u1 again where you had this I mean guys who do string theory and who thinks about you know string emission calculations They told us, you know, there is another u1 there must be another field And you must use a theory which is at least you want the force supergravity And then there's a very nice physics which happened Essentially you have some singular configuration of war factors and the some other singular configuration of this extra field and Even if both of them are singular Their singularities cancel and the metric only depends on this particular on this particular combination and the full solution is smooth So it was really it was really a nice input from string theory hardcore calculations Which told us, you know, you have to look for this particular microstates and made our life easy And the fact that exactly the same field which string emission calculation and precision holography spit out Comes out to be to make our life smooth, you know, this was really I don't think it's a coincidence I really think it's it's indicating that we are zooming in on the right on the right physics So and by the way, just to impress you, this is the largest family of solution Known to mankind the solutions of two very its functions of two variables which are arbitrary So you give me any function of two variables you want I give you the solution So it's really it's you know, this is really the largest cost of solution known to mankind And this is this parameter I was telling you about Now You can also get super start I'm going to go a bit faster because I want to get to non-super symmetric black holes You can also get super starter which have a long throat Which are again, which look again like like like flat space and ads 3 and then they have a long ads 2 throat You can also count the entropy, but I'm going to go a bit faster because I mean, you know It's really that you know using these configurations You can you can really argue that you have the right you have the right ingredients And essentially there's a lot of work to do but you know I think it's more at the level of dotting the eyes and crossing the t's rather than, you know Understanding what the fundamental physics is I think we really have the we really have the fundamental physics Now okay, this I'll go through there's a lot of stuff about the MSW I want to get to the So essentially the super the supersymmetric microstate story which you have is that again We have this huge number of solutions and they basically are dual to some CFT states Which which would look to be typical. I mean again, we have many arguments We have many arguments about them and moreover there are two calculations Which are done at intermediate stage between stormage of alpha with zero gravity and our calculation with full gravity Which also are supporting that you know black or micro states come from these particular configurations and Essentially, I think I really think We are on the right track Now I want to get two words about quantum gravity in ads2 because again everybody and their brother and their brother nowadays is doing ads2 So I k everybody's trying to understand why is quantum gravity in ads2 And you know, what's the implication of these things for quantum gravity in ads2 Now, why is it difficult to do quantum gravity in ads2 ads2 is the most generic near horizon geometry of Extreme or black holes and when you have an ads2 space and you want to add an excitation in ads2 You find that you cannot this excitation either screws up the uv or screws up the infrared you cannot have localized excitation in ads2 and The fact that so we either get the uv singularity or you get an ir singularity There's something in scik which I think is related the fact that the four-point function in scik is not conformal invariant This is really coming because in a sense when you have an operator you back react it You destroy the conformality you destroy the ads structure the ads structure does not remain when you take an object and you back react it Now this is the nice this is the story about ads2 which is a nice and beautiful story But we know that in string theory singularities are solved and you have 20 years of experience of like, you know Singularity solving in string theory and you know how singularities are solved They are solved by extra strings and brain dynamics, which involves extra dimensions And if you look at and if you look at the typical microstates which we have again We have we have some microstates and these microstates have a long throat have a throat Which can become longer and longer and longer and there's a nice limit Which one can take which is pretty straightforward which involves essentially chopping off this flat space and negating a solution Which is just ads2 and then ending up in some cap And essentially all the black hole microstates which we have been building until now all this super strata And all these skillings all the solutions which have been building for the past, you know, 12 years Especially the ones which are which have a long throat, which is again Which they get a very important feature which I think which I think is crucial all these solutions They have a limit in which they become ads2 And moreover all the information in these solutions again The solution I built by some Fourier modes and some fluxes and so on and so forth All the information all the all the counting of these solutions goes over into ads2 So if you solve this problem which we have that, you know We're trying to build all the black hole microstates to get the entropy and so on and so forth You also solve the problem of ads2 gravity because you're getting all these solutions Which have again an ads2 throat. So for example, this bit is a microstate again There's a limit in which you basically have all the microstate structure and then you have just have ads2 Going on forever and you basically find all the states of quantum gravity in ads2 So there's a there's a quantum mechanics dual to ads2 And each and every ground state of these quantum mechanics is dual to one of these solutions So if you solve the problem if you solve the problem of black hole counting using these microstates You also solve again ads2. You also understand what's happening in ads2 So how did this avoid this fragmentation issue? This is not fragmentation. This is basically fragmentation comes from From taking two supersymmetric black holes and and moving them at a distance Here you basically have just a bubble at the bottom of the space So in fragmentation you have an ads2 which is breaking up into two ads2 Is the topology in the ir which is different in fragmentation You really have an s you really have some space which is breaking up into is like breaking up into pants This is really closing up in this topology. And then if you want to put a wave for example in this ads2 They can coming back to here If you want to put a wave in this ads2 you can put it But you know the way you know if you put some particle here to just have some way But you know the wave is going to be eaten up by this topology So, you know, it's pretty straightforward to get it's pretty straightforward to get to get this ads2 You know to put particles in this Uh, so essentially again the story for supersymmetric is that again I have so much of alpha There are two calculations in between and we have our our microsets configuration But it looks like again for supersymmetric black holes All does the entropy comes from again horizon as configurations which remain horizon as all the way through there's no horizon There's never any horizon And essentially again, so again for supersymmetric black holes We are basically arguing that the that the black hole solution is just a thermodynamic Explanation and there's a similar story for supersymmetric for non supersymmetric and extremal black holes Which I'm not having time to go into I mean there's a lot of work Which we've been doing also with monica and other people about the curl black holes There's many there's many there's a similar story that again when you have this black holes You can replace their horizon very easily But again the question which tibba was asking me before okay black holes are beautiful and they're supersymmetric But they are extremal And if you think about the extremal black hole peros diagram, which you know, I'm just giving you a slice here What you are saying that external black hole peros diagram you have this singularity And we are basically saying that this region doesn't make any sense the region which is which is here In blue and therefore there's some quantum effects coming out and destroying the horizon, you know here However, this is not so strange if you think about it, you know from a from a gr perspective You have a you have a singularity here the singularity can emit, you know Elephants and the elephants can destroy the space time in these regions So some people are saying okay great you guys are doing some amazing stuff for extremal supersymmetric black holes Where and again this happens, but this is not so strange, you know people in gr You know people there are many people in the gr community who hate extremal black holes Even when storm engine and wafa had their nice black hole Microscopic counting they say are you are you string series are just doing extremal black holes But you know real black holes are not extremal So this is just a freak of nature and you know, non-extremal black holes are going to be much more different and they'll have different physics And so again, what's the big deal? This is some hardcore gr people They they say okay, what's the big deal about doing only extremal only extremal black holes The big deal about these calculations is that if you look at you again quantum information arguments That you know there's something at the horizon in order to preserve unitarity These quantum information arguments are telling that you only have a black hole. This is the naive space time You could have the singularity resolved in two ways You could have the singularity emitting some garbage and you know destroying this region of the space time But you know you still have an outer horizon and you still have you know some space time between the outer and the inner horizon Or you could have this you could have the singularity And you could have the space time actually messed up here And again, this is backwards in time from where the singularity is forming But in order to resolve in order to preserve quantum mechanics, the structure needs to be actually here So when you go from extremal to non-extremal Instead of so the structure which is here at the inner horizon It should go all the way to the outer horizon. It should not stay stuck to the inner horizon Again, if the structure only stays to the inner horizon We've saw you know, we found a nice beautiful formal question We asked that if I a nice beautiful formal question But not the real question about black holes, which is again, how can I find the structure at the outer horizon? And however to do non-extremal black holes And that's complicated because you know, how can I argue that such a structure one has to build lots and lots of such solutions You know again for supersymmetric black holes I told you that I can build a huge amount of them for not supersymmetrical life is much harder And the reason is that you know, you have second order non-linear PDE is in the best of cases And it's just Einstein equations which would like you know function of two variables You know it took curl, you know 50 years to find the first even a black hole solution What we're talking here is like you know way way way more complicated stuff. And you know, it's very hard to do so There's a Romanian proverb, which is you know, do not pray to the saint who doesn't help you And essentially when you cannot find all these solutions, there's a way to do it Portability so you can say that I have a I have a supersymmetric microstate Which is again a supersymmetric black hole microstate I can add an object which is called an anti-brain to these solutions And this anti-brain is actually going to give me a metastable minimum And this configuration of a supersymmetric solution with a non-supersymmetric object with a non-supersymmetric probe Will actually be a microstate of a near supersymmetric black hole So you can go you can go not far from extremality, but near extremality I can I can find near extremal microstates and I can actually argue That you know, essentially when you have these near extremal microstates, they have the right features For example, these anti-brains can have something called brain flux annihilation There are very common in string cosmology those of those of you who do string cosmology Who know about string cosmology these anti-brains are the bread and butter of string cosmology And essentially these anti-brains will decay by brain flux annihilation Which corresponds to Hawking radiation and you can find black hole microstates again of near extremal black holes using this method This is one way to go around and it's again cheap, you know Cheap, but you know we're getting a huge amount of microstates of near extremal black holes There's another way there's another Romanian proverb Which is that you know when a when a bird is blind sometimes god makes its nest And sometimes you can actually be lucky and actually Guillaume and Stefano's got mad at us They actually found a system when you can actually find the non supersymmetric non extremal solutions Which can actually be solved By solving a linear system. This is quite amazing. I still don't know how they did it I mean it involves in only nilpotent algebra algebra and stuff Which only Guillaume understands and I think Stefano's also but it's really some amazing piece of stuff There are some solutions which which one can build in gravity in five dimensions, which are non supersymmetric non extremal And we're able to build such solutions which have you know multiple cycles and so on and so forth And these solutions in principle they can take us far away from extremality. They can really give us non extremality I think the most recent one which Guillaume and David and Stefano's building has like you know 18 non extremals So, you know one can really go away from extremality by a finite amount. They're not doing only near extremal by like, you know 700% Okay, 700% Okay, so you can really go away from extremality like really a big distance away from extremality And those are again solutions which are built not by solving Einstein's equations of two variables But by solving a subsystem which is actually linear and which one can solve in a pretty straightforward way Okay straightforward means like you know, you know tons of tons of work and you know those guys you can ask them I mean, you know, they've been they've been on the computer, you know doing all these calculations I mean and you know the solutions are mega are mega big but one can go away from an extremal It's really amazing. I mean if you know if I had thought then again It's really this problem that you know, you have no idea and sometimes, you know You bump into you know, you are really lucky and this particular system is really amazing That you can really find solutions away from extremality Non-super symmetric with multiple cycles and the question is okay How far from extremality can I go hydrogenic the others want to be do they correspond to antibodies? Looks like there's a link between them and antibodies. It's really it's really that you know this This field so right now we really have solutions We really have there's a really a machine a machinery to go away from extremality and to generalize all this story to non-extremal black holes So expect those to be very unstable. Yes, and I'm coming to that very important very good question I'm really coming to that so for near extremality What we expect at least is that we have resolution backward in time And we have a way to argue that even far away from extremality again You have this kind of structure you are replacing the black hole horizon But not only the inner horizon but all the way to the outer horizon you are replacing this with with some structure Now the big question which I asked you before why is this Why is this thing not collapsing and I told you about you know this paper by Gary Gibbons and by nick Warner explaining that you know, there's a mechanism and you know, there's basically some There's a there's a way to to argue that that that that this is the only way to build back on microstates What's happening is the following you have some cycles and there's a flux on them The flux is quantized you have 17 quanta if you make the cycle very small the energy of the flux on it Becomes big So what's keeping the cycles from collapsing is the fact that you have cycles with a quantized flux on them Which don't want to shrink because shrinking cost energy So even if there's a gravitational attraction Putting you in there's a flux on this one on these cycles Which actually pulls you out and is the flux which keeps you from collapsing And the nice thing about this paper by gibbons and Warner is that you can argue that you know, essentially from If you want to build Solutions of gravity or of super gravity you can argue that the only mechanism The only mechanism to avoid collapse in a semi classical limit is by doing bubbling You cannot build a black or soliton otherwise you must have topology black or solitons need topology And this is really the level of a theorem So this is really like you know hardcore calculation and it's not only about supersymmetric black holes This is also about any type of black holes you want So if you want to build any any black or soliton which has a semi classical description Those guys tell you that the only way to do it is to have bubbling So when people say that you know, they are replacing the black hole by some quantum fuzz or by some devali Things which have like you know quantum effects and so on and so forth and we you can always say okay Great. I'm replacing the black hole by some big quantum mess Oh great There's a quantum mess if in this quantum mess any state in this e to the s dimension quantum mess is classical Or semi classical which hopefully one expects again. I don't want to want to have e to the 10 to the 90 states I don't want all of them to be quantum and with no classical limit for for any of them if any state is going to be classical It must be One of these solutions if any state is semi classical if so you can say okay All states are going to be quantum and so on and so forth maybe But if anywhere in this Hilbert's plate, there's one state which is classical it must look like this So this is so so so this theorem is again very It's very powerful from from a from a low dimensional perspective. There's another question. Okay Why do I avoid this no go no go theorems about about about this matter if you think about compactifying the cycles with fluxes Two strings into this is this is all done in m theory This is all done in in 11 dimensions if you think about going to four dimensions or to 10 dimension string theory on on a calabi all the reason why these fluxes don't collapse is that When you compactify the solutions you end up with some objects Which have negative mass and negative charge from a low dimensional perspective in string theory. They're nice They're just you know some some bubbles in m theory, but when you go down to type to a string theory They become negative mass negative charge objects Those objects are common in string theory But again you have orienti folds which for example have negative mass and negative charge But this is why they don't collapse the reason why they don't collapse from a 4d perspective Is that they really have they're they're a highly unusual form of matter Which again comes from compactifying string theory is very natural to obtain this kind of unusual form of matter when you compactify string theory to Four dimensions again when you compactify these smooth solutions, but it's not the kind of matter Which would normally put I told you before that you know you have to put something in the horizon all the stuff falls in Yes, all the stuff falls in except this stuff And this stuff again comes from compactifying cycles and it really has negative mass and negative charge This is really the feature of this stuff and in string theory is perfectly natural If you want to replace the black hole horizon by usual stuff, you know by dust or by by stuff Usual matter doesn't hang around. It just falls in the black hole You need to have this highly unusual type of matter To stay at the horizon, but string theory provides it for you The string theory really provides you this kind of matter which can stay at the horizon And what about other black holes? Well, if I give you this pair of diagram and ask you what does this black hole represent Is it really a near-extremal black hole or is it the Schwarzschild black hole which has one electron? Answer is is the same pair of diagram The Schwarzschild black hole with one electron has exactly the same pair of diagram as a near-extremal black hole so If you argue that in string theory this can happen for near-extremal black holes It's also possible that, you know, maybe this also happens for Schwarzschild I don't have microsits. I don't have a solution again. Hopefully We go home and David, you know, and stephanos. We are pushing towards, you know far away from extremality And, you know, hopefully we're getting there But at this point I don't have if asking for a Schwarzschild microsit microsit I cannot give it to you So the only thing which we have are near-extremal and some far away from extremality But again, if you just think about the pentose diagrams, it's exactly the same the same pentose diagram If this phenomenon happens in one corner of string theory, why not happening in some other? I mean, I expect it to be I expect to be there just one second and I'm finished so And again, then you can ask, okay, what about the real panels that Schwarzschild solution? Well, I mean if this happens, you know, just take the electron away and you get the Schwarzschild solution So that's not a big state. So right now essentially there are four approaches again, you know Just to just to just to get a bit of a global view There are four approaches that pure black hole states have no horizon On one hand, you have information theory based arguments Mathur first, which is 2009 and then amps Following that arguing that there's a firewall or not And but that's a secondary question again, you know, the question the real question is, you know Do you have garbage of the black hole horizon or not? Do you have something there? Anything? And the arguments based on information theory that you must have something there The arguments based on generic ADS-CFT, Kiryakos is against But you know the arguments based on genetic ADS-CFT that, you know, a black hole There should be something A typical state should have non-trivial waves and therefore there should be It should have no spherical symmetry and therefore no horizon the arguments using ADS-CFT But just very generic arguments. Nobody really has one solution And those are really agnostic of the theory these arguments they could happen and look onto gravity They could happen in whatever dynamic triangulation you have those are really generic arguments having to do with any theory of gravity whatsoever That something must happening at the horizon must be happening in the horizon Then you have two string theory ways of doing it. You can either see Say, okay, let's take strommage of alpha. I'm a tweak coupling I'm following microstates from week to strong coupling towards the black hole regime And again some calculations called black hole deconstructions Distring emission calculation which Rodolfo and Stefano Giusto and David Tartan are doing There's a Higgs column map which I worked on with with yarn and shear and other people There are many there are many approaches arguing that when you when you go from weak coupling To the gravity regime of parameters you have some configuration which grows Some results are are inconclusive But you know, I think there's an overall there's an overall feeling that you know this You are going to get this kind of thing and the other option is to just build all this black hole microstates Which again are forming are forming black hole solitones And the mechanism I gave you is bubbling again. You have these classical solutions and so on But to answer Elias's question which he asked me, okay, what about curvature? Why do you know that you know, this is not going to be stringing stuff This bubbling mechanism what you have you can actually extrapolate it when the when the bubbles become very small This goes into something called brain polarization which you can also study So there are basically many regions of parameters in string theory where you can study this phenomenon and It's so if this So this bubbling support mechanism actually extrapolates even even far away from the region where it what you trust Low energy low energy low energy supergravity So that's basically so that's basically the situation and The question which everybody asked me is like first of all, you know, all the microstates Going to be classical answer is I have no idea. Hopefully not. Maybe yes What I hope is that the classical solutions will form a basis To understand some genetic features of the Hilbert space. That's my hope. But again, that's some that's a calculation to be done It's not something which I can just which I can just tell you now. Okay. It's classical or not I have to calculate the black hole entropy. I don't have we don't have yet. We don't have yet yet There's another question which has to do with costasis question About anti brains and about these solutions of non-extremal black holes We've been saying this is clear for many many years that anti brains are tachyonic and therefore they are very bad for cosmology And therefore you don't get that they see the landscape and you know We've been doing all this all this work on anti brains arguing that anti brains are tachyonic And for cosmology, this is horrible because it implies that a universe built with anti brains is unstable But for black hole, this is perfect because when you are Looking at the non-extremal black hole you actually expect instabilities And the reason is very stupid if you think about the d1d5 system you have left movers and you have right movers Which are giving you the non-super symmetric microstates those guys annihilate and they annihilate and they emit Hawking radiation So there's a generic argument by mature that essentially Non-super symmetric microstates must be unstable. This is really a it's a feature. It's not a bug If they are not unstable, then you are doing something wrong and jmart is unstable For example, if there are many calculations arguing that and the ones which we're finding with goyam and davin and Stefanos are also unstable So you can really argue that all these non-super symmetric microstates must be unstable And but that's something which makes a lot of sense in adcft Again, you have right movers and left movers. They annihilate. They can emit Hawking radiation But what's the point of counting subtle points? I mean you want to count class They are spanning the Hilbert space. So if I can span the Hilbert space Life is a classical It doesn't matter it's still a state I'm trying to span the Hilbert space. So first of all for non-super symmetric. I cannot count anything I'm just just to be just to be But I think the point is, you know If you want to understand, for example, you know, I have the CFT in the CFT I can build some non-super symmetric states If I can emit the CFT non-super symmetric states with bulk Configurations and I can argue that, you know, they have the same features and then, you know I can argue that adcft tells me that, you know, all the typical states of the black hole will be such Such configurations And essentially adcft tells me that if I have a non-extremal microstate it must have Instabilities Then it will disable Yes, and jmart, for example, if you take a decoupling limit it becomes pure ads Of course the instability is only visible when you glue this microstate to flat space It's not visible if you look at the in the in the in the in the decoupling limit is gone That's, you know, very good point. So jmart, for example, if you take the decoupling limit There's no more instability. The instability goes away. The instability only comes when you take jmart and you glue it to flat to flat space Very good point. I didn't even What about non-linear? I'm done. I'm basically so what about non-linear instabilities? And again, this is something which people have been arguing that, you know, essentially the solutions have a non-linear instability There's a cft calculation that, you know, this makes sense There's a big question everybody's asking kind of fall through the black hole drinking your coffee You know, is it really you don't have firewalls or they have fastballs or what's going on? And or they go sprouting the horizon size and that's three options You can either analyze infinite density shells which are kept at the horizon by the tooth fairy Because again, nobody has any support mechanism or you can look at the solutions We have which have a support mechanism and you can try to ask this question Or you can modify gravity by weird terms and analyze the horizon again Many people are doing many weird things But the one to do is you know to actually use the actual solutions And so far the answer is going to depend on this configuration depends on how many of these guys are how typical they are What's the entropy? It's really a lot of calculations which one has to do We cannot answer these hard questions by just hand waving and by arguing that I'm replacing the horizon by something and something else And so far I don't see any reason why these solutions can let you go through David Disagrees There's a question about you know, can you see this structure when you have gravity wave collisions? Answer is maybe the structure of the horizon when the two when the two black holes approach They start messing up the structure of the horizon if something is is at the horizon And these two black holes are collapsing You may have extra terms in the gravity wave in the gravity wave Calculation and you know this can have this can mess up this cursor table calculated so That could be you know, so this is even even something which is which which may be Visible so again to summarize we've seen the string theory has configuration Which can hover above the horizon and they have again topology of laxies And for supersymmetric microstates again We see that you know we have all these calculations that you know really you really have you really have This picture is correct for non-extremal non supersymmetric. We have a similar story And when you go to non-extremal you have to go to near-extremal or far from extremality with some help Maybe there's some other ways of doing it using numerics or inverse scattering and so on and so forth And again, maybe if this term if this physics of the horizon has an effect to truncate a principle calculate It maybe it will affect gravity waves or for example make the supermassive black hole formation in the early universe More likely, so I leave you here You stress that our classical states are the only states that could be constructed with focusing on ground But would one expect that quantum effects are the dominant effect? I don't know how to do any calculation which involves quantum effects and gravity at the same time So people are saying okay quantum effects quantum effects Quantum effects everybody's trying to replace the black hole by quantum effects of the horizon size There is no calculation involving quantum effects and gravity at the horizon scale which anybody has ever done But what I know is that when you have quantum stuff again, everybody tries to hide I mean in this problem I mean there are many many people who want to replace the black hole by something and they say no It's all quantum Great you have e to the s Hilbert space e to the s dimensional Hilbert space if in this Hilbert space There's even one solution, which is classical It must be this So there's no but but but again if So the problem is if you just do it in in some random theory And you have a classical solution coming out if it doesn't have d brains to give you low mass degrees of to give you this growth With with with the horizon size if it doesn't have e to the s entropy if it doesn't have all these features It doesn't work So that's again, I'm very adamantly against arguing that oh you have quantum stuff and then just hide behind the quantum stuff I'm not disagreeing with that statement. Of course. I'm agree. I'm agreeing with that statement I'm a bit worried about is stressing that classical states dominate Any mechanism? I don't know. It's a calculation. It's a calculation. I don't know The classical states will form a horizon as you say no no no no no these classical states will not these classical states involve topology and fluxes They're not from a horizon Sorry, what stops the problem to change the positions? Oh in this particular example, which I'm computing I have I have a huge number of states And I just calculate the tunneling into each and every one of them and I get a number And if my system wants to go into those states, you know, what can I do to it? But there are assumptions behind those calculations Of course, no sure but again all the states I have I mean I have all these solutions And my my tunneling my system wants to tunneling to them So I mean the the question to ask is I kind of where does this That was the what does does the collapsing shell want to go and the answer is to not go into horizon it will go into this Gary you had a question Yeah, I just wanted to know your response to Harvey real and his friends who's saying that because of the So-called evanescent ergo Region that your solutions will be unstable, which is something that dick and I did not address Oh, no, so the point is the evanescent ergo region comes from okay I have it here. This is the question about non-linear instabilities So they argue that there's an evanescent ergo region and therefore if you look at the linear perturbation There's no instability because you have a supersymmetric solution But when I look at the non-linear perturbations So if you look again if you think about you know two perturbations on top of each other Then you get an instability But this makes perfect sense because again, what what's what's a non-linear instability is really You put a linear perturbation you back react it and then you put another perturbation on top of it But once you back react it you go you build a non-extremal configuration So the fact that essentially this non-linear instability is there Is the same as saying that all the non-extremal microsets are unstable But that's exactly what I want the d1d5cft tells me that exactly what I want I want the non the I want the non-linear I want all the non-extremal microsets to be unstable because they have right movers and left movers on this effective string Which annihilate which can hit each other and emit closed strings So my my understanding of this instability. I was very happy when they found the result For me this result just confirms the intuition which again matur has been telling us for a long time That non-extremal microsets must be unstable and that's again a cft calculation And those guys are just confirming it using again this more fancy technology So i'm again, it's a result which may which may made me very happy Despite what they wrote in the paper But what's the time scale of these I mean would they make astrophysical black holes go away? much faster Here for example, so the problems I can know this is all supersymmetric and near supersymmetric The only thing which I can do is a bit like in adsqcd. I can make some estimates based on you know charges and so on one thing which I know about the timescale is that Okay, what they have it is if you think about for example, two black holes collapsing In the early universe and there's a big problem in the early universe about how to form supermassive black holes Because when you have a black a bunch of black holes going around each other They collapse they know let's say they're all solar mass black holes They collapse they form a few black holes But then the other ones get thrown out of the system and you never form supermassive black holes If for example because of the microstructure you have another term at the horizon like some friction term for example This is again huge string mess at the horizon scale if this term has some friction for example Then when two black holes go around each other There's another channel to eat up the energy the energy can be eaten up in these open string modes living in the system And therefore the collapse may be more efficient than therefore the gravity wave signature may be different And it may be easier to form supermassive black holes These being sent there's a calculation to be done which I haven't done So I need to really build a few of those guys and to really understand this calculation. I have another calculation. So