 Popular physics books tell us that when an electron and positron collide, they annihilate, turning into pure energy, balderdash. Most of the time they just turn into photons. How pure is a photon? Some kind of mongrel remnant of the standard models SU2 and D1 gauge groups, left for dead by the wayside, by the Higgs mechanism. Not so pure. Pure energy is energy contained in the curvature of space-time itself. Black holes on the inside of it, and gravitational radiation going off to infinity. So, today for a truly pure energy talk, please welcome from the city of music, from the once and future capital of spines, our most theoretical visitor yet, Daniel Gruberler. Okay. Yeah, thanks for this fantastic introduction, Yasha. It's a pleasure to be back at OIST. And today's this talk is going to be about what you don't see in this picture. So, I dissected my talk into three sections. The first is water black holes. And that part is suitable for last year primary school children. So, eight to 10 year old children. So, if you're a physicist, then you won't learn anything new except maybe a way to address this question so that your children understand it so that they can explain it to their friends as well. And if you're not a physicist, I hope that you take away the main message from this part, namely what is a black hole? Okay, then I'll spend a little bit of time on the question how to discover black holes or how to make the invisible visible. And in the final part, I talk about black holes in the holographic principle. I'll do so again in a mostly non-technical way, but there will be one slightly more technical slide. But again, even if you're not a physicist, I think I can try to convey what the main message here is. And if you have any questions, I don't know if you usually interrupt during the colloquium or at the end, but feel free to ask questions anytime, and you can also ask them in the end, of course. Okay, so let's start with the first set of questions. What are black holes? Before addressing this, I want to answer a more existential questions, namely, do black holes exist? And spoiler alert, the answer is going to be yes. But that question, when I was studying physics in the 90s, was still somewhat controversial, at least to the extent that Nobel Prize winners like Tini Feldman made statements like black holes might just be figments of the human imagination. So in the 1990s, it was not generally accepted that black holes do exist. But they were pretty soon accepted by pop culture. As an example, I show you here the pretty black hole of the Dragon Ball genre. And part of the reason why it took a while for the community to accept the existence of black holes is because we couldn't see them and seeing is believing. So even when I started lecturing black holes in the 2000s, the best I could do to convey what a black hole is visually was to show some artistic impression like this. So what you're supposed to see is some visible star and its mass and energy gets sucked away by this black hole, which is in this dark region here. And it accumulates in this so-called accretion disk around the black hole. And that's the part that we can see. And from measurements of the accretion disk, we can deduce whether or not this invisible object is actually a black hole. Now, much better than an artistic impression on actual data. And the most accurate data in the form of a simulation was produced by keep phone and collaborators for the movie interstellar. So this is the famous black hole gargantua, which is a protagonist in this movie. And you can see already quite a bit of difference from this computer simulation to this artistic impression. So what the artistic impression shows is how the accretion disk is, namely, essentially a flat disk like the rings of Saturn. But what this computer simulation shows is what you actually would see. And what you see here can be summarized in a simple slogan, namely you can't hide behind the black hole. So the part of the accretion disk that would be behind the black hole, you can see it due to rotational lensing effects. And this produces this ring here. Now, we don't have actual photographs with the same resolution as this amazing simulation here, but still there are actual data that are similar to this. And I'm sure you have seen this iconic photo, which appeared in April 2019. So this is the first photo of the shadow of a black hole. If you care about details, it's a black hole M87 with a mass of 6.5 billion solar masses and a distance of 53 million light years from Earth. And this picture will appear a couple of times in my talk. So we'll spend some time exploring this. Okay, so the short answer to this question is, yes, black holes do exist. We can make the statement with a similar amount of confidence that we believe in the existence of quarks or other elementary particles. Okay, so let me now explain what is a black hole and I'm using this analogy that was introduced by Bill Unruh in the 80s. So let's assume you're somewhere in the Yambruh National Park and you go to the mountains. You find this mountain lake and in this mountain lake you have a bunch of fish. You have some slower fish, which look a bit like the Greek letter alpha. And then I have faster fish, which I've turned to 90 degrees, so they look a bit like the Greek letter gamma. And these fish explore the surroundings. So they swim through this lake and eventually encounter that the lake ends in this mountain river and the river becomes steep and steep and ends up in the waterfall. But the fish here are oblivious to this fact. They only know the lake. So to explore the surroundings to send some daring but slow alpha fish down the river. And that fish swims down the river, finds new algae, finds the pebbles, hopefully no predators, and then returns to the lake and explains to the fish what it has found. Now that works only if the fish can actually swim back. So if the speed of the current of this river doesn't exceed the maximum speed of that fish. And let's assume that this happens at this point here. So I drew a line here, which I call alpha barrier, but it's not a physical barrier. So it's a line, pretty much in the same way that you draw red lines on geographic maps to indicate borders. You see them on the map, but when you're there in nature, of course, you don't see any red lines. So this alpha barrier is precisely the location where the speed of this river is equal to the maximum speed of this fish. So what happens when the fish passes through this barrier? Well, the fish cannot return. As soon as the fish passes through, eventually it will end up in the waterfall. So that means if the fish above here only test the river by sending down the slow fish, they will get knowledge about the river only up to this alpha barrier, and they won't know anything beyond this. So then the fish above here may speculate what happened. So maybe there's some drama here. There's some firewall who burns the fish or there's some fish eating dragon or something else terrible. Or alternatively, they may speculate that nothing exciting happens here and the fish is just too slow to return. And in order to test this hypothesis, they send down the fastest fish in the river. So one of these gamma fish. And that fish indeed can swim through this barrier. So that nothing exciting happens there. The river just before the barrier looks almost the same as the river after the barrier. And that fish can continue to swim down and explore further food sources or interesting stones or whatever and explain the fish up here, what it has discovered. But this also only works as long as the speed of the current doesn't exceed the maximum speed of the fastest fish. Let's assume this happens at this line here. I call this the black hole barrier or the horizon. So this is pretty much like the alpha barrier, but it's a barrier for the fastest fish in the lake. And since it's a barrier for the fastest fish, it's a barrier for all the fish. So no fish that swims through this barrier can ever return back to the lake. So that means if the fish only use other fish to test their surroundings, they can map out the whole river up to this point, but not beyond. So for the fish up here, this boundary looks like a semi-permeable membrane. So fish can swim through it in one direction but cannot return. Now interestingly, it's not physically a membrane. So a fish that just floats here will not notice that they have passed this point of no return. They will just pass through and no drama happens. But still, a fish that is swimming through is doomed because no matter what the fish does, after some time, the fish will end up close to the waterfall. And that may be unpleasant. There might be strong currents or eddies or whatever. And eventually the fish falls down the waterfall. So to translate the metaphor into actual black hole physics, this whole construction here, the lake and the river and the waterfall, this is supposed to be an analog of spacetime containing a black hole. The fish up here are, for instance, us, observers on Earth, observing the universe. The fastest fish in our universe is light or gravity, so photons or gravitational waves. We are among the slow fish. And this point of no return for the fastest fish, this is what we call the black hole event horizon, or just horizon. And we can map spacetime in principle until relatively close to the black hole, but not beyond the black hole horizon. And inside the black hole, again, somewhere in the center, there might be some drama analog to the waterfall. In physics language, we call this a singularity. And yeah, we don't have any direct knowledge of what happens inside the black hole. Okay, so that's the essence of what the black hole is. I'm going to elaborate how to detect them. But if you have, if you're not a physicist, especially, and you have questions on this picture, then feel free to ask. Yes. Can you please explain what the white hole horizon is? Yeah, okay. So I was not going to cover that part of the picture, but since you asked. So this is where the way you could continue the metaphor, except that we have not observed any white holes in nature, and we don't know if they exist. But just to explain what happens here, white hole is essentially the time reversed version of a black hole. So black hole is a region where you can enter, but you cannot exit. And the white hole is a region where you have to exit, but you cannot reenter. So a little analog of a white hole is if you just turn on water and it falls in a flat basin, then you can observe that there's a flat region. That's the white hole region and the less shallow region. And in this less shallow region, you can excite shallow water waves and can transmit information in this way. But this information can never enter the shallow region. So a fish who survives this fall down the waterfall would exit this white hole horizon, so could swim further into this river and into some other lake here. But if the fish tries to swim back up the waterfall, it won't succeed because at some point the speed of the current again exceeds the maximum speed of that fish. Any other question? So in one simple phrase, a black hole is a region without escape, like the vortex in the lake. Good. So before moving on to how to discover black holes, let me address a few more basic questions. The first one is what is a black hole made of and that was hinted already by Yasha, but okay, let's not spoil it. So everything seems to be made of something. Planets are typically made of heavy and light elements like a whole earth. Stars similar to a sun are mostly made out of light elements like hydrogen and helium. But a black hole is actually mostly made of nothing except space and time, besides the very center. So I indicated this here by this dashed line. So this is the horizon of the black hole. Again, it's like a red line on a geographic map. It's not the boundary that you physically see. You cannot stand on a black hole. And everything that falls into the black hole will accumulate in this waterfall. So in the center and the singularity in the middle of the black hole. Okay, some other interesting question that is often asked is how big is a black hole? And probably a third of the expression astronomical numbers. So in astrophysics, we often have to deal with very large numbers. So it's kind of amusing that one of the most extreme objects that we know in astrophysics, namely a black hole, has a very everyday life size. Namely, the smallest black hole that we know is about the size of Naha. So it's not gigantic. It's about 10 kilometers. And indeed, if you place this black hole at the center of Naha, it will not even rejoice. Multiple black holes may reach almost twice or may even cover us. And the largest stellar black holes that we know about the size of all Okinawa. So you can imagine the typical size of black holes is more or less the sizes of Okinawa. But that's only true for stellar black holes. Yes. So this is the border of your circle, exactly the black hole horizon that you described? Yes, yes. I just wanted to point out that the precise building we are in is listed on the map. It's not just a waste of light. Okay, yes, yes. That's fine. It's really light for here. Okay, cool. Good. This is only true for stellar black holes. So for black holes that essentially emerge at the end of the life of stars that are similar to a sun but a bit more heavy. But they're also bigger black holes, namely the one of which we've taken pictures and they can be of the order of a couple of billion kilometers. So the size of the black hole whose first picture we've taken is about the size of our solar system. So that's a graphic taken from the webcomic XKCD. Okay, so now we know some basic facts of black holes that do exist and they are a bit like semi-permeable membranes. You can pass through them but not exit. Let's now address the question how to discover black holes or how to make them visible visible. So I'll present only one slide of this, but it's packed with some information and a bit of history. So the history starts in 1783, about 100 years after Newton's gravity law was discovered and the fineness of the speed of light was measured. And John Mitchell was the first person to put these two ingredients together. I'm not going to read this whole article to you but you can just Google John Mitchell black holes and you find various pages of his seminal article on this. So he considered star with the same density of the sun, sorry, but 500 times its size. And he calculated that the escape velocity from such a star, so the velocity you need to escape from it with a rocket, would be the speed of light. So that means not even light can escape from such an object, so that was the Newtonian picture of a black hole. And he even made some remarks on how to observe such an invisible thing because obviously it's not so easy because, well, light cannot escape from it. But he already mentioned the possibility that maybe there's some visible partner nearby and from the anomalous movement of this visible partner, it could deduce some information about the invisible object, about the black hole. And this is in essence how we measure or how we discover most of the black holes. Okay, then for a long time, nothing happened. Next milestone was 1915 Einstein finishes general activity, which took him almost a decade. And then Schwarzschild only took a couple of weeks to find the first exact solution to general activity. And amazingly, this is a black hole solution. So that is an indication for a fact that I'm going to elaborate on a bit later. Black holes are in fact very simple objects, not just very simple. Classically, they are arguably the simplest objects you can imagine. And I'm going to explain in which sense I mean this. Okay, then, well, I'm skipping many developments. So I fast forward half a century. The first observational hints of a black hole were made in the mid 60s of the past century. So this was the system signals X1. This was a so-called binary system. So that's a system like in this artistic impression where you have some invisible object. You have some visible object and you have an equation disk and there's jet emission. You have x-rays you can deduce from the x-ray spectra some properties of this invisible object. And in some cases, you get strong hints or strong evidence that this invisible object is actually a black hole. The term black hole was popularized by John Wheeler in the same decade. And that led to lots of developments in science fiction and movies. Some of them very good like interstellar, some of them very crappy like this one. And yeah, next milestone was in my year of birth, 73. Hawking calculates that black holes actually evaporate at a tiny temperature. And the formula for this temperature was immortalized by putting it on Stephen Hawking's tombstone. And then I skipped quite a bit to 2008. Getz and collaborators discovered the supermassive black hole in the center of the Milky Way by observing the Kepler orbits. In a few minutes, I'll show you a movie on these Kepler orbits. Then 2014, Kip Thorne and friends simulated black hole equation disks for the movie interstellar. So this is this black hole gargantua that you've seen already. And a big breakthrough was in 2016, LIGO measured gradation waves from a black hole merger. So that was both the discovery of gradation waves and the new way to discover black holes. And then 2019, the Venturizing Telescope took this iconic photo of the black hole shadow. And 2020, the Nobel Prize went to Penrose for black hole theory and to Getz and Genssel for black hole observation. So probably I'm preaching here to the choir, but let me nevertheless make this remark. Basic research often is not a sprint but a marathon. If you look at the timeline in 1783, John Mitchell first pondered about the possibility of black holes. And then 200 years later, the first black hole related Nobel Prize was awarded to General Secker. Then three decades later, the next black hole related Nobel Prize for LIGO basically was awarded to Bearish, Thorn and Weiss. And then three years later, the next Nobel Prize to black holes to Penrose, Getz and Genssel. Okay, so what are possible answers to the question in this title here, how to make the invisible visible? Some of these options I think you can transpose to other sciences. Some of them are fairly obvious. So the first option is one that I like, but I can see that it's not sufficient because after all physics is an empirical science. So the first option is we see them visible through thoughts mathematically. And this is pretty much a summary of the early days of black holes that was the only option available to us. The second option is we see them visible through interactions with the visible equation, this physics or the Kepler orbits. So let me see if this works. So what I'm going to show you is not a movie per se. It's actual data. So it's not a simulation. It's real physical data spanning a decade of observation. And what you see is the movement of stars in the center of our galaxy. You can see the star line from the early 90s to the early 2000s. And when you zoom into the center and you trace the movement of some of the stars, you see beautifully the Kepler orbits. And what you can see is that some of these orbits come very close to the, let me show this again, come very close to the object around which all the stars evolve. And you can convince yourself that this is not a lot of room available. A large number of invisible stars here, the only reasonable object you can place there is actually a black hole. So that was the discovery of the black hole in the center of our galaxy. Now the third option is you see them visible through other sensors. So metaphorically through hearing, although you don't literally hear black holes. What I mean in this context is you can try to detect black holes, not by using light in one of its forms. So x-rays or microwaves or whatever. But rather you use instead some other means, namely in gravitational waves. And this is possible since 2016. And the final option is you see them visible, at least for now the final option, maybe in the future there will be additional options available to us. But for now this is the final one. The last option is we see them visible through the shadow that it makes on a visible background. And this is what the Einstein horizon telescope did when it took photos of black hole shadows. Okay, one could give one hour lecture on each of these ways to discover black holes, but I want to end my summary here. If you have any questions on this detection part, then please feel free to ask them now. Yes. In all of the appearances of black holes being artistically or data stimulation or analogies. They seem to appear kind of in a disk shape format, which has a particular type of symmetry in one dimension and it loses symmetry in another dimension because if it were symmetric, it would have been something like a sphere. I don't know if there is any explanation for why it looks like a disk. You mean why the metal creates around in the disk. What, what, why do we have any kind of symmetry even in one dimension. Is there what why isn't it distorted shape rather than being a disc nicely floating in the. It's not precisely flat this so it has some extension also in the other direction. Regarding symmetry is what I can say is the black hole itself is symmetric so the most general black hole that we know is a so called Kerr black hole, and that has actual symmetry so it has rotational symmetry to some axis. And in some cases, the equation this tends to be aligned with this somewhat aligned with the black hole access. And, well, if you're just asking why does matter creed in the disk. This you can already explain in your tone and gravity that's a feature of stability it's similar reasons why matter creates in rings around Saturn. So, yeah, that's that's that's classical Newtonian gravity reason. So, you don't need generativity to explain this, this kind of shape. Having said this, the dynamics of this equation this is quite complicated to you need more than just gravity. There are also viscous effects that also. You need to use magneto hydrodynamics also magnetic fields are important. So, there's no first principles calculation you can easily do with paper and pencil so you have to rely on numerical simulations to describe the physics of these equation discs. And due to this processes in particular the heating up of the matter. We have a mission of x rays and this is what we observe in our telescopes and this is how we can identify various fit parameters like what is the mass of invisible object, sometimes also what is it spin and other parameters to describe this invisible object. And in some of the cases, we can be sure enough that the invisible object has to be a black hole. And there are other cases, so I should say that not only black holes lead to this equation discs you could also have a neutron star in the center of such an equation equation disk. And it's not always trivial to discriminate between these cases. Okay. Any other questions on this part. All right, then. Let me move on to. So, this book is intended for PhD students or researchers who want to give lectures on black holes. So it's not at the level of my talks it's not for the general audience, or even for scientists from other fields interested in black holes, but it's intended for people who really want to get their hands dirty so there are lots of exercises and details on black hole physics. And this book was written together with my colleague shine check Jabari from Tehran and appeared last year in spring up. Okay, end of commercial. Let me come to the last part black holes and develop it principle. So this will be the part that is more related to what I'm actually doing in research and also why I'm here. And it has to do with the fact that you may have further namely black holes of interest for quantum gravity sometimes it's even said that black holes may play a similar role for the development of quantum gravity as the hydrogen atom did for the development of quantum mechanics. So, I want to explain at least mention why this is the case. It has to do with apparently paradoxically properties of black holes. If you neglect quantum mechanics, then black holes are arguably the simplest microscopic objects in our universe. All the properties are determined if I just give you three numbers the mass, the spin and the charge. And these are essentially the same quantum numbers that determine all properties of elementary particles. So you can think of black holes as gigantic elementary particles if you want. And there's really nothing that could be simple. So, by contrast, if I want to give you data on, say, the sun, if I just want to tell you what is the temperature of the sun, I have to give you one function of four variables. I have to explain how the temperature varies as a function of time, there are various solar cycles, how the temperature changes when we move into the interior of the sun. So, as a function of the radius and also how the temperature changes as a function of the angles on the sphere, the colder and hotter spots on the sun. And then I've just explained to you what the temperature of the sun is, so then I still need to explain or describe all the other properties of the sun. By contrast, if you want to know the temperature of a black hole, well, if you know the mass, the spin and the charge, you can just calculate it. And that is true for all observables related to black holes. They are amazingly simple. Now, this is only true if you neglect quantum mechanics. If you take into account quantum mechanics, the story doesn't just get a little bit more complicated, but black holes are arguably the most complicated objects that could exist in our or any other universe, and that they are the most entropic objects. So, if you're a physicist, well, then you know what entropy is. If you're not a physicist, you can think of entropy as information if you want. Okay, so what does quantum mechanics tell us quantum mechanics tells us that black holes evaporate. So this was calculated in the seminal work by Hawking that I mentioned earlier. And even before Hawking's calculation, Bekenstein, using Gedanken experiments, was already suggesting that black holes have an entropy. And the way that the entropy of black holes behaves led Toft and Susskind in the early 90s to suggest that black holes behave like a hologram. And this is what I want to elaborate on. This is to do with the famous Bekenstein-Hawking or black hole entropy formula that the entropy of a black hole scales like the area of the horizon. And that's the only formula that I want you to take away from this talk if you're a non-physicist. So since it's so important I displayed again in bigger letters, this is the Bekenstein-Hawking entropy. Why is it remarkable? Well, I tried to find, again, a simple analogy. So since entropy has to do with information, well, a basic entity that contains information is a book. I googled for some book on OIST and this is what I found, the OIST by Willard. I was not able to uncover what's the content of this book, but I assume it has some content. If you want to know, well, how much information is in this book, it's not sufficient to look at the cover. The cover doesn't tell you how much information is in the book. So a good measure of the information in the book would be, you know, the number of pages. You can estimate the amount of information at least roughly if you know that the book has 100 pages. Well, then you can more or less guess how much information is there. If it has 1,000 pages, you would estimate it has about 10 times more information and if it has only 10 pages, it has about 10 times less information. So, again, just looking at the cover is insufficient. We need to know how many pages the book has. And this should not just apply to books, but basically to any object that contains information. So you should look at the volume of that entity and depending on the volume, there might be more or less information. But for black holes, this is not actually the case. In general, this is true. You need to know the volume. You need to know the number of pages of a book if you want to judge how much information is there. But for black holes, the Bacon-Steinhawken formula basically states that you can judge the book by its cover. You just look at the cover and that's all the information there is. You can look into the book. There might be some information, but it's going to be redundant with what is written on the cover. And that's why this formula is remarkable because it's quite different from the way that entropy behaves for standard thermodynamic systems. So let me elaborate a little bit on this. So let's compare the entropy of a gas with the entropy of a black hole. So the entropy of a gas is, for instance, the entropy of the air and this lecture hole. So if I would double the volume of this lecture hole, I would essentially double the amount of information, so I would double the entropy. We call this property extensivity. It just states that the entropy scales like the volume. Okay, and what is the volume? Well, the volume is some length scale to the power of the number of special dimensions. Assuming that we are in three dimensions, this is just a statement that the volume scales like length cubed. So if you want to calculate the volume of the cube, it's just length times length times length, so length cubed. Okay. The entropy of a black hole is different. It scales like the area, so this is length to the power d minus one. So in three dimensions, the area is just length times length, so length squared. Now, since it may be confusing what we precisely mean by volume and area, I present this basic table here. So in various dimensions, volume means something different from what colloquially we mean by volume. So in one dimensions where we just have a line, the volume is actually the length of this line. So it's length to the first power, so just length. In two dimensions, the volume is what colloquially we call area, so it's length squared. And in three dimensions, the volume is what also colloquially we call the volume. It's length cubed. And if you compare various data in this table, you find that the area in three dimensions, which scales like length squared, is the same as the volume in two dimensions. So up to some geometric factor, these two expressions are identical. So you have length squared here and length squared here. Why is this important? Well, because when you compare the entropies, you observe that the corresponding entropies match. If you consider a black hole in one dimension higher than a corresponding ideal gas. So if you consider some gas in two dimensions, the amount of information contained there scales in the same way as if you put the black hole in one higher dimension. And this is what motivates the holographic principle. So the holographic principle lifts this basic observation to a principle. So it states that the theory with gravity in D plus one dimensions is equivalent to a theory without gravity in D dimensions. So for instance, a theory of gravity in three dimensions, so D would be equal to, would be equivalent to a theory without gravity in just two dimensions. And that explains the name holographic or hologram in the title here, because it means that gravity behaves like a hologram. So you can view it in two ways, either as a three dimensional entity or as a two dimensional entity. So here I summarize, at least in words, some consequence of the holographic principle. In my view, it's one of the most fruitful ideas that we had in theoretical physics in the past three decades. And what it states is that the number of dimensions depends on the perspective. And we can choose to describe the same physics using two different formulations in two different dimensions. And the higher dimension formulation is a theory with gravity in general a quantum theory with gravity. And the lower dimension formulation is a quantum theory without gravity. Okay, these are just words. And in case you're unhappy with just words, I sacrificed one slide for the connoisseurs. So here I give two examples for entries in the so-called holographic dictionary within the so-called ADS-CFT correspondence discovered by Marlesin in 97. So what do I mean here? You have two different formulations of the same theory in two different dimensions. So that means you should be able to provide a dictionary between quantities you calculate in one formulation and quantities you can calculate in the other formulation, and they should match. And this dictionary was established in a specific context by a group's agreement of Polyakov and Witten for so-called correlation functions. So these are certain mathematical quantities you can calculate and they give you insights about quantum field theoretical observables. So here's an example. So this is, well, this is not only for the experts. So this is a five-point function of the stress tensor flux components in the two-dimension conformal field theory. If you are non-experts, the only takeaway here is that you calculate some expression in two dimensions, you get the result. And the result is essentially given by a function that I can write in one line. And then you can calculate another observable in a gravity theory in one dimension higher. You get an expression and that expression involves exactly the same function here. So these quantities here match precisely, but they were calculated in two different theories. This was calculated in a two-dimensional conformal field theory without gravity, and this is calculated in a three-dimensional gravity theory. The other example I present briefly graphically is so-called entanglement entropy. So entanglement is an important resource for quantum technologies, quantum computing and so on. And like with any other resource, energy or money or whatever, it's useful to quantify it. And entanglement entropy is one out of many possible ways to quantify entanglement. And this is a quantity that is often very hard to calculate in quantum field theory. And Rion Takyanagi showed in 2006 or conjectured in 2006 that there's a very simple holographic way to calculate this observable on the gravity side, essentially by calculating geodesics. So these are shortest lines in gravity. So a calculation that is very hard is mapped to a calculation that is so simple that you can give it to a third-year physics student. So it amounts to calculating things like areas of soap bubbles or shortest lines in some curved spacetime. All right. This is just a glimpse. Of course, there are infinitely many other observables that you could calculate and that people have calculated. Fine. So this is amusing, but you could say so what and why are there so many papers on this? Well, the answer is that these holographic correspondences have led to numerous applications. And pragmatically, this is so because it provides a tool for calculations. So we have now two options to describe the same system. And if you have two options to describe a given physical system, you can just pick the simpler one. Sometimes both will be very complicated, so there's no use. Sometimes both will be simple, so then you can choose either of them. But then there are also cases where one formulation leads to very simple expressions and very simple calculations while the other is practically impossible. And then these holographic correspondence can be fruitfully used to solve problems that otherwise you couldn't solve. And while this is not universally true, but in many instances it is found that the holographic correspondence maps complicated calculations to simple calculations and vice versa. So this is why these two can be very useful. And I present two classes of examples without getting into details. So example type one is you map a strongly coupled quantum field theory, which is very complicated to describe to weekly coupled classical gravity theory, which is very simple to describe. And the other type of examples is you map quantum gravity, which is very complicated to weekly coupled quantum field theory, which is rather simple. Both of these types of applications have been developed in the past two decades and there are many examples of calculations where you have this map between complicated and simple. I will not spend time on exploring all these calculations instead in the remaining couple of minutes. So I want to focus on some key questions, namely how generous the holographic principle, does it work in our universe? And if yes, how does it work? And if no, when does it work? Okay, so this is one of my long term research goals to find out how general the holographic principle is. So, so far, the best developed implementation of the holographic principle is the so-called ADS-50 correspondence, which I've managed. And just to give you a glimpse what kind of geometries this involves, ADS doesn't stand for attention deficiency syndrome, but for anti-desitter. And it means essentially the wrong, so negative sign of the cosmology constant. So ADS-2 essentially looks like a Pringle. So if you have never seen this, this is what anti-desitter is, Euclidean ADS in two dimensions. I even copied here the mathematical code. So if you watch this on YouTube, you can just copy this code and incident mathematical and draw your own Pringles. So this kind of geometry features in the ADS-50 correspondence and it requires negative cosmology constant, which is usually denoted by the Wiglet of London. Now, in particle physics, we don't care about anti-desitter usually, we like flat space. So in particle physics, we want to set lambda equal to zero. So we have very simple planar geometries. And if we want to apply holography to a universe, then we need a positive cosmology constant. So we need the sitter space. So this is what we can do. And this, and this is what we would like to do. So this question here is very general and usually with general questions, you have to break them down to make some progress. So one particular instance of that question is does holography work without the cosmology constant? And here I just flashed some random publications that deal with this question. So they have appeared in the past decade. And there was even a workshop here in the OST Quantum Gravity Unit during the COVID time, precisely on this topic, it's called flat asymptopia. So especially in the past decade, there was substantial progress, but this is still very much an ongoing research endeavor. So we haven't fully cracked flat space holography. There are some instances of holographic correspondences or at least of glimpses into holographic correspondences, especially in lower dimensions. But we are nowhere near the same sense of rigor or establishment as in the case of the ADS-CFT correspondence. So this is still work for the future. The other question that you could address is does holography work with a positive cosmology constant? And that's a question I'm frankly too scared to address, but I'm very happy that people here at OST are not so scared. So this picture I actually took from the OST Quantum Gravity webpage, and there were also interesting developments in the past decade on this digital holography. Besides these two questions, there are numerous others, which I just mentioned here briefly. So you could study lift sheet holography, shredding holography, high spin holography, near horizon holography, celestial holography, corollan holography, near ADS-CFT holography, warp data holography, etc. So as you can see, there are numerous research avenues when breaking down this big long-term question how it generates the holographic principle into sharper and more manageable and also more precise questions which you, in some cases, can then address. So in case you are a student, either in this room or watching this on YouTube, I think this provides numerous research avenues. And since there's a lot that we don't yet understand, students are very welcome to join the adventure of finding out how general holographic principle is. Now, let me make a second commercial break. So, especially for students, I will give an OST lecture series on asymptotic symmetries, which is a gravity way of analyzing aspects of holographic correspondences. You find this announcement on this webpage here, and it will be a set of eight lectures, and the first one starts July 31, so it's always Mondays and Thursdays. All right, this brings me already to the end of my talk, and I decided to let JetGPT give the final word. So this is what happens when you ask JetGPT to finish your black horse talk. I'm just going to read what it wrote. Ladies and gentlemen, thank you for being a stellar audience today, as we explore the fascinating realm of black horse and holographic principle. Now, before we reach the venturizing of this colloquium, let me leave you with a light-hearted observation. Did you know that physicists love word play? It's like a quantum superposition of cleverness and groans. So here's a pun for you. Why don't black horse go to parties? Because they always suck the energy out of the room. Thank you, and remember, even in the vastness of the universe, a little laughter can transcend space and time. Enjoy the rest of your day. Thanks. There's also a microphone here, but I'm not sure if this... Thank you for the talk. Could you just explain... I mean, I think you touched on it, but I didn't understand completely why... You can't get a... why the holographic principle doesn't suffice to get a working quantum theory of gravity? Why it doesn't suffice? I mean, you gave some examples of mapping quantum gravity to other theories with the holographic principle, but... Well, some people would say it suffices to define what you mean by quantum gravity. You could take the viewpoint that I just accept the holographic principle, and I define quantum gravity by its field theory dual in one lower dimension. So I take the viewpoint, I accept the premise, holographic principle is assumed to be correct. Then I just map quantum gravity to a quantum theory without gravity, and we have a lot of expertise in dealing with quantum theories without gravity. Quantum field theories are reasonably well developed and well understood. So if we take this viewpoint, we could claim that quantum gravity is solved. This is, however, not completely satisfactory because you would still like to address certain apparent paradoxes that appear when you naively apply quantum mechanics to gravity. So a famous example is so-called information loss problem where you would deduce naively from putting together black hole physics with quantum effects that black holes destroy information, and according to quantum mechanics, this shouldn't happen. So this seems to be one of these sharp paradoxes that we like to understand. And we would like to understand it in more detail than just saying this paradox is solved by the ADS-50 correspondence, or this paradox is solved by holography because we know that quantum gravity is mapped to a theory without gravity, and such a theory should preserve information, so therefore there's no paradox. So yeah, I guess the short answer is that we would like to fill in some of the gaps or some of the details, how quantum gravity works precisely, and we would like to understand this not just from the field theory perspective, but also understand how this translates to the gravity side whenever it's possible. The other aspect is that so far the best developed correspondence is the ADS-50 correspondence. We would like to understand quantum gravity not just in an ADS-50 context, but also in other contexts, in particular in our universe, because quantum gravity is probably of importance for the very early universe, so there we shouldn't rely on ADS-50, but instead develop something like the pseudo-holography. Does that answer your question? I think so. Okay, yes. Thanks for the nice talk. Back to my third question. All of which come from a non-expert point of view, of course. So you partially explained, at least to my understanding, that there is a partial symmetry for a black hole. And I'm just wondering if you place your telescope in a particular standpoint and look at all possible black holes that are in your view, would they all represent themselves with a similar direction of symmetry? No, no, no, no. They can be tilted in all directions and the creation disk, sometimes you watch it more edge on, sometimes you watch it more from above. So you might be worried that many of the creation disk we might not even see, but if we actually were to take pictures because of the fact that you can't hide behind a black hole, we would even see a creation disk if we are looking at it rather edge on because of gradation lensing effects. And my follow-up question is then in the analogy, there was this white hole horizon. Yes. Did not appear in the rest of the talk. Would whatever associates to the white line horizon, white hole, whatever line horizon, to talk about, would that also manifest any kind of symmetry similar to what you observe about black holes? So what I can say about white holes is that we don't know if they exist in nature. So we have no example of white holes in nature. They appear as automatically whenever you find an exact black hole solution where you neglect the way how the black hole was generated. And the so-called eternal black hole, like the solution that was found by Carl Schwarzschild, that geometry describes not just the black hole, it also describes a white hole. So in this naive approximation, a black hole always comes with a white hole. But when you check how a black hole is actually formed in nature, it is formed from collapsing method typically. It is a star that has burned out at the end of its lifetime. If it's heavy enough, will collapse on its own weight to a black hole. And in that situation, there is no white hole in the picture. There's only a black hole that is being generated. So again, the short answer is we don't have any strong reasons to expect the existence of white holes in nature, though they might. And if they do, you can think of them as the sort of the time-reversed version of a black hole. And they literally the complement of the black hole in the space. Like if you have a black hole, then the complement is what emits energy and hence can be viewed as. Yeah. I mean, compliment, this is not a bad word for this. So in this hypothetical solutions that I mentioned, the eternal black hole solution by Schwarzschild, for instance, also by Kerr, you have, in addition to the black hole horizon, you have a white hole horizon. And you can think of the black hole horizon as being an entity that is in the future somewhere. So when observers pass through it, they are trapped and the white hole horizons the corresponding entity in the past. Yes. Yeah, I don't know. Let's do the thing with the hands again.