 Welcome everybody to our current Latin American webinar of physics. It is my great honor and pleasure to introduce Dr. Diego Rubiera Garcia, which is currently a Richard Fellow at the Institute of Astrophysics and Space Sciences at Lisbon University. Diego got his PhD in 2008 from the University of Oviedo in Spain. Then he moved to France to Observatory de Paris Moudon. Then he went to Oviedo again, then to Brazil, to Paráva Federal University. Then he moved to China at Fudan University, and now is currently, as I said before, at Lisbon University. Today he will talk about surviving from a journey into a black hole. Diego is an expert in extensions of general relativity, metric affine spaces, black hole, non-singular solutions, and what is perhaps called mathematical properties of general relativity. Please remember that you can ask questions over using, like, Twitter. You can also write your questions over the YouTube channel, and then at the end of the transmission, we will tell your questions to Diego so that he can answer all your questions. Okay, so Diego, let me... Can you hear me? Yes. Okay, so now you can share your screen. We can start. Okay, so I start at the window. Can you see it? Yeah, perfect. Okay. Okay, so shall I start? Yep. Yes, your final? Yes. Go ahead. Okay, okay, so... Okay, so first of all, thanks to Alejandro for inviting me to this new way of giving a seminar. So it's my first experience with these webinars. So it's a great idea to research this research material with people around the world. So today, so I choose this fancy type of... because I think it captures quite well what is the intent of this research that I've been doing in the last maybe four or five years. So actually, this is a small part of a larger piece of research as my investigation, which is standing general relativity by a lot of different motivations. So we have been using black holes as a way of testing mathematical, physical, phenomenological deviations with respect to general relativity. So this talk I'm going to focus on a very particular aspect of this black hole, which is essentially trying to ask the question of what would happen to a physical observer that crosses the even horizon of a black hole. So what would we do to fight this observer? When you ask this question to general relativity, so you find an answer that makes little sense. So I'm trying to explain why this makes little sense and why it is motivated to see general relativity through what is their hopes. They have tried to keep the technical use to a minimum and some passages of the talk cannot be helped. So you will see some involved equations so I will try to explain these quite simple terms. So I hope that the level is reasonable enough for most of the people to follow. So right now we have plenty of evidence reporting that black holes are real objects in the universe. So the latest piece of evidence that we got was the verification of the existence of gravitational waves 100 years after the formulation of general relativity. So the first event, black hole detection, was in 2015. So it was explained, so it was compatible with general relativity expectations for the merger of two black holes. So basically what many people, many groups around the world are doing about these traditional waves is so they allow, numerically, the Einstein equations using different kinds of black holes. So most notably this merger depends on the masses and spins of the black holes and then they produce characteristic signals which is what we can see here, these blocks. So here, the reconstruction of the signal, we see very clearly the three characteristic phases of a black hole merger, which is the approximation of the phases. So it is fully compatible with the expectation of general relativity. At the same time, two years later, in these two events, this refers to the gravitational wave detection, which refers to the electromagnetic wave detection, so this event, set of two black holes, the merger of two black holes solutions, is associated to the merger of two neutron stars. This offers new windows, not only to try to explain important phenomenology regarding the neutron stars, such as the equation of the state, incidental stars, but it also offers a very interesting playground for testing deviations for general relativity in this field of change. So this is very relevant for modified theories of gravity that propose that general relativity is not the ultimate theory of gravitational interaction. Many of these theories have been proposed using cosmological considerations, in the sense that they are constructed as alternatives to the lambda CDM model, the standard cosmological model. So the results reported by Lisa Birgo on satellite collaborations about the observational gravitational waves and the associated electromagnetic radiation have offered important insights on these modified theories of gravity or, as I said, on the compatibility of these theories of modified gravity with gravitational wave observations. In particular, the fact that the gravitational waves and the electromagnetic waves were distributed here on Earth with a few seconds difference tells you that they travel in these two waves traveling back approximately at the same speed because, given the far distance from these objects to any difference on propagation of these waves exists, this will have been manifested by different rival lines of these two waves here on Earth. So the fact that we approximately receive them at the same time has translated into experimental constraint of one part into 10 to the 16 parts. This is such a strong constraint that has allowed us to pull out a large number of cosmological models. So a few days after this discovery of this gravitational wave from the New York Stars, so there were many papers on archive making an examination of different theories of gravity to see whether they are compatible with this oscillation of the model. In particular, they call your attention to this nice paper where they have some papers where they are very nicely cosmologically viable theories. They still are viable from the point of view of gravitational wave observations and those are no longer viable. At the same time, there are other observations from traditional waves like the fact that another paper released by Ligur and Leigo they found that they can only find gravitational polarizations indeed, the other relativity predicted that in vacuum there are only two degrees of freedom in the polarizations of the gravitational field are propagated. But there are many modifications of the other relativity in the existence of other polarizations. These polarizations have not been found and actually really scalar polarizations has been reported to be solved too loud by these observations. So other polarizations have been featured experiments which will allow to put additional constraints upon these modifications of the other relativity. There is a need of search for new models in order to understand the theoretical of the number of Leigo consequences. In this answer, Wood's guiding principle is given perhaps the Schwarzschild Plan 4. So during the case, there have been a number of mathematical developments that have been now formulated as theorems of singularities. This theorem tells you that in general relativity is the ultimate theory of classical gravitation then the emergence of space-time singularities are unavoidable within this theory. It's a simple example as I said Schwarzschild solution this is just the solution representing the gravitational field mass n here. So actually it took 45 years to fully understand what this solution has to hide and actually has been found that there are two regions, one and two with the solution so basically region one is the solution external to even horizon but in appropriate coordinates you can extend this solution between even horizon to the center of the solution. So this is nobody's and this too that's the classical structural problem for the solution. The problem with this is that this solution is not truly satisfactory. If you want to know exactly what happens at the center of the solution you find a number of problems related to the fact that the Schwarzschild solution is a part of the solution of space-time which is and the field equation of the solution are most often at the center of the center of the solution. Indeed, if you try to associate a point particle at the center of the solution as generated at the additional field of this object this cannot be the destiny questions with this source are not consistent. If you insist on trying to build this building a model of additional collapse you find that the matter that falls into the inner most part of region one of region two the energy density of the matter field there will grow without bound as the collapse grows on. If you try to associate also the Schwarzschild space-time you will find that the Schwarzschild also diverges but at the end of the day you get at the center of this object you get divergences, infinities, similarities there is something strange happening at the center of the problem. So despite the observational success of the end of the activity there is at the theoretical level a fundamental problem related to the lack of predictability and determination when you try to understand what's happening in the most region of the problem. Actually it's difficult to explain what the specific similarity is because this is something fundamentally different from other kind of singularities we are used to in physics because as opposed to other kind of singularities such as the divergence of the raw field in classical endodynamics. These singularities do not correspond to some divergence of fields according to a fixed space-time actually this singularity is how it depends on the structure of the space-time itself. So because of this it's difficult to capture the notion of what a singularity is and the theory of singularities offers a little clue about this. The value of a singularity will give you information about what a singularity actually is. So it's natural to think that it seems in general relativity and gravity it's a matter of the curvature of the space-time something is going is wrong has to be related to something going in with the curvature of the space-time. So in the sense one would be tempted to study these places where curvature of the scalars could grow up so we are dealing with scalars in order to avoid artificial singularities that could be avoided just by a change of basis. But there are several problems with the grow-up of this characterization in terms of the grow-up of the scalars if you have a look at Wolf's book on general relativity it's explained very nicely why stabbing the blow-up of curvature is simply unsatisfactory because it's doesn't exhaust all the possible kinds of pathological behavior but to me the most important point is that the most reliable the results that we have about the singularities lie on the singularity theory and these theories there are there is no reference to these scalars. Actually this theory makes it to a different concept which is something which is called geodesic completeness. This concept is important because to highlight geodesics are associated to the free form of physical small servers but no geodesic is associated to the propagation of light rays and transmission of information. So the mind in the geodesic completeness in your physical theory means that you impose the physical principle your theories of nature there will be there exists no possibility of creation of something from nothing or disappearance of information into nothingness. So imposing the principle geodesic completeness means that if a space time is geodesically incomplete then it's singular but the other way around is not true. So in the case of Swartz in the rest of our solutions it's very clear to see why they are singular. They are geodesically incomplete so they contain at least one incomplete geodesics. So in this theory information can be created out of nothing or disappear into nothingness. The cities cannot be this is clearly a reasonable principle and the power of the singularity still lies on the fact that they implied that in general relativity this singularity is for cure and the very general assumptions on the schedule of space time and the behavior of matter fields and in particular does not depend on particular significance that you have assumed in order to build your solution. Despite this law still most of the community still insist on using the characterization of bounded scholars to build what they call the aurora plajos. So this idea of bounding the curvature of the scalars have produced a lot of approaches but I have only underlined here a few so one falls a long scale effects in order to come from a lot of gravitational waves etc even more fundamental approaches in theory of gravity in any case in our research we have said this need of going in order to try to address the problem with space time singularities. So our approach in this sense is more modest than fundamental approaches we still have said that gravitation some other or is related to the curvature of this time so we built up our theories we told jets that are with basic blocks are the metric and the connection from the connection you build a demand tensor and make a contraction of the demand tensor either with the metric or itself you build different objects in order to construct your theory of gravity in the simplest case where you build your Lagrangian mass simply the scalar curvature so this is the contraction of the metric with the rigid tensor so this is general update but there are much more possibilities here then you have several options here because you have two independent fields here have the metric and the connection you can impose the connection it's compatible with the metric otherwise it satisfies this equation which means that your connection will be given by the crystal for the symbols of the metric this is exactly the situation that you have and this approach to build these theories is called the metric approach there is a problem with this approach when you go with an activity so if you build the field equation for this action you have a standard variational procedure so you have a variation of the metric so you get this set of equations here you have the standard number in the tensor on the right hand side and you have new objects here the problem with this, because of this problem derivative here in general this set of equations for the general activity we have second order field equations here we have fourth order equation and because of the pressure on this term you are introduced to this because of these fourth order equations we usually have course like disabilities you have a potential incompatibility of these theories with solar system experiments there are some exceptions like global law theories of gravity even in FFR theories of gravity you have higher fourth order equations but there are no cause but there is a way you can do things better if you still keep to the idea that metric and connection are independent objects all you have to do here in what is called the metric find a flow is to make a variation of this action with respect to the metric and with respect to the connection independent you make this variation you have the variation with respect to the metric and the variation with respect to the currents because these two objects are independent so you have two independent set of equations at first side it doesn't look like a very big deal because instead of having one set of equations then you have two set of equations but playing wise with these equations they can be the cause in this form so what you have in this form is on the left hand side you have the instant tensor of some metric which we call here the auxiliary metric but this auxiliary metric is related to the space time metric in this way so there is some artificial object four times four object here you are in four space dimensions and the trick the important point about these theories is that this object here depends on cell only on the energy momentum tensor that appears here and because this object appears here are also inside the gravitational lagrangian everything that you have here on the left hand side of the field of equations is a function of the energy momentum tensor these equations are just Einstein equations with a modified energy momentum tensor on the right hand side so it somewhat it mimics the philosophy of the analogy and because again this metric here is related to the space time metric via a matrix that depends on the matter field so once you solve this Einstein equation you go back to the space time metric using these algebraic transformations and then you find the final solution for the problem but these equations are manifestively second order and because in vacuum they give you exactly the another activity so there are no cause there is automatically compatibility with solar system experiments and also with gravitational wave observation made so far also if you use these equations you put your gravity lagrangian to be the one of the Einstein Q-delagrangian then you get that your field equations for this case are also general this metric of high formulations is completely compatible with general relativity when you choose the Einstein Q-delagrangian but if you go beyond general relativity you get these Einstein like equations and then you have a new playground to play with these fields so there are many scenarios that you can play with and because in this talk we are interested in black holes so we are going to deal first with spherical asymmetric solutions so any static spherical asymmetric solution with a loss of generality can be written this way with two independent functions that are specified in some coordinates you can always write a line element this way the other examples for spherical asymmetric solutions are the one of Schwarzschild and the one of the Einstein Q-delagrangian where the radial function trivializes and you have this for the other metric function these solutions correspond to black holes if this function has at least one zero or Schwarzschild which is always the case depends on whether this mass and charge satisfies the constraint so you can do the same in this metric of high fields of gravity that you just described spherical asymmetric solutions so if you consider a quadratelagrangian like this one where you have the pitch scalar squared you have the pitch scalar here and the pitch scalar and the pitch squared right? you can also include the contraction of the the remand tensor with itself but because of the value of the topological invariant can be always be removed in favor of these two invariants just by by casting these two constants to all the variables so using these equations that I mentioned before and using the inhalation for this theory of gravity metric of high field of gravity you can solve these equations and you get that these functions of the Schwarzschild and the Schwarzschild transform into this flow there are two differences first this matrix function so it's a little bit more involved here essentially this function will tell you when horizons are present in this theory it's depending on mass charge and the value of this parameter you will have different numbers of horizons it's even more important the behavior of the radial function as I said in the case of general relativity the radial function normalizes but here it doesn't they have something new, it's the object so there is a new radial coordinate which is the scale in order to deal with dimensionless coordinates core radius here depends on the charge, depends on the business scale that I have introduced here, depends on solve the mass whatever and if you study the start of this solution you find that for large distances you will recover a reasonable solution but if you are near the inner motion region of the solution it turns out that for a finite value in the radial function the metric function takes this form for instance here and then you have one over our behavior here it's clearly different from the behavior that we talk in the case of resonant motion solution so the inner motion region of this solution are completely different from the resonant motion one and indeed if you analyze the behavior of the radial function what you get is this kind of stuff so this function here is depicted here in dimensionless form and what you see here is that here everything like this looks like you know the activity with the reduction of this metric to this and most but when you get out of the center so the radial function gets to a minimum and then bounces off actually this is absolutely compatible in the specific behavior of wall holes so wall hole is a kind of solution that also exists in general relativity but in order to build it in general relativity you have to violate any conditions because of these these solutions are divided and physical but in the case of metagraphy in quadratic modernity as present this is not so because the way we consider a electromagnetic mass well fit in any condition so this is satisfying all the physical principles in this sense but there could be troubles here the minimum value of the radial function where the wall hole probe is located because in general curvatures divergences will arise so this is on our question once weather the impression of this curvatures divergences that the wall hole probe is a solution such as so then we go to the full arsenal that we already know in general relativity about how we can test the regularity of the solution the first tool in this arsenal is to go to geodesic so the geodesic question can always be asked this way metagraphy theories there is a potential interpretation problem because you have the components of the connection here but we have in principle two different connections that is the connections of the amplitude method that is the crystal for symbols and natural set of geodesics there is also so consider geodesic associated with independent connection so which one you should choose here if you assume the Einstein equivalence principle and the fact that matter is not coupled directly with the independent connection which is what happens in all settings then the physical geodesic will be those of them if you use the other connection what will happen is that you can always recast this equation this being the the connection but there will be new turns here that will appear this is not so if you have only coupled the matter to the method and not to the connections that you do so because we are using a spherical space time there are two consequences which is the angular momentum and the total area and you can always rewrite this geodesic equation that is the geodesic tangent method that is why this equation is exactly what you get in geometry except here there is a new factor this function is not the one that you have here on our team this is the workhouse of geodesic this comes from the px here for zero corresponds to new geodesic the same photons and for one it corresponds to physical method so in order to see whether this geodesic solution is geodesically complete or not we integrate this equation in the simplest case which is geodesic so this is just photons heading directly to the workhouse of geodesic this is the geodesic integration when you depict it so you go up here for an asymptotic infinity you have closed the workhouse of the road in general relativity you will get to zero geodesic stops there but here because of the workhouse you can close without any problem so this parameter is geodesically complete for any value of mass and chat in general relativity as I said the high parameter stops here there is no possibility of extending there the reason our solution in general relativity is singular here it is not singular in the sense of geodesic complete if you also make the same analysis here non-drabial also for time like geodesics here you can in this paper you will find that all these geodesics are complete so all these solutions are geodesically complete for all values of mass and for all values of chat ok there are more tests but there are more tests that you would not like another test is what is the physical implication of curvature invariance because curvature invariance is in these solutions at the one whole code my code very large is my potentially induced very large tidal forces that leave any physical body apart which is called the spagatization effect so this is due to different forces between the feet and the head of a potential this tidal forces will also stretch this observer in the radial in the angular direction so at the end you have an spaghetti because it's launched this way and stressed this way actually this intuitive idea can be put in mathematical in rigorous mathematical terms by modern observer in terms of a congruence which is nothing but to assume that this particle of the body is free falling up of its own but because of the existence of tidal forces each geodesic can fill a force that can hit the body apart so you can obtain you can find three Jacobi vectors that tells you which is the relation between each particle of the body the choosing of these vectors arbitrary but you can define a volume that is not arbitrary this algorithm is basically the terminal for the three Jacobi vectors that you have chosen in the congruence and there are several criteria that tell you according to this guy some other that when you approach the chromatic region where true or true it was very high if this volume goes to zero then you have what is called a strong type or a classic type in work the correct as I said tidal force theorem the observer apartheid is in the ideal direction so this will imply that causal contact is lost between different parts and the observer is strong so even if individual pointless point without size points of the geodesic can cross to the one fork it potentially means that standard observer will get away apart and they will not survive to the transit to the ground when you apply the same criteria there are these vectors and this volume in these modified blockers that you saw you get the result that the volume instead of going to zero close to infinity and this result has not a proper interpretation with this so you need to something in order to see what are the physical consequences so in this very technical detail paper what we did intuitively was the model again these objects using a congruence and then two parts of the body allow when a body is crossing the problematic region and see if this round tip between these two parts of the body is causal or whether it can be effectively down below the state of life and what we find is that using a moving coordinate this is actually what happens it's part of the physical observer near the one fork is in causal content with any other part but this means that physical interactions standing in the body might be effectively transmitted and are not inevitably destroyed upon the transit a third criteria is that instead of using individual geodesics or physical body made up of geodesics use weights so make tests with weights with the one fork example you can take a scalar way equations or the ideal angular and temporal modes approximations near the one fork and then you can compute any scattering experiment transmission and reflection factors and when you do this is that you can compute these factors transmission factors no problem everything seems to be well posted part of the signal process and the one fork part of the signal is reflected and curvature divergences are not affected by propagation they are affecting geodesics completeness but this is another test that the solution spots the fourth test that we try is that geodesics are complete but because of the due to the principle of general covariance that helps you or servers with any arbitrary motion are physically equivalent to any other one any observer with any arbitrary motion should also have a complete path otherwise it could happen the situation where all geodesics in the sense that all pre-folding physical observers are complete paths but if you are in a spacecraft and you switch on your engines with some acceleration or acceleration you could find an incomplete path in order to avoid this pathological situation you need to describe the motion of an accelerator of servers static, spherical, and symmetry of this path with some acceleration and then you get the standard geodesic equation which are these two terms you get this modified by another term that depends on the feedback acceleration here you can apply this completely general formula to the models I was mentioning before and then you pick up some new term here this integral that appears here which is this one and then again you do the same you explore all the spectra of mass and charge and accelerations pressing your model and what you find this paper is that all the paths of all accelerative observers with finite acceleration no matter the value of the acceleration mass and charge can be indefinitely static so all the paths of accelerative observers in these solutions are complete because we are running out of time so I just go to the conclusions of this so the question is my SQS graph provides a journey to one of these modified plazos replacing the Dresden-Dostos solution with general relativity so we have done this first we realize that after crossing the inner horizon both photons and stable servers might get to the 1.0 infinite proper time and then we use four different criterias of Dresden completeness or trajectories or diagonal Dresden the tidal forces do not necessarily need to be physical observers because the parts of the body are at all times in physical in causal contact the scattering of waves of the 1.0 is well posted and the path of accelerative observers no matter the value of finite local acceleration they are always complete because of these the photons are no singular so there is no need of evoking any cosmic sensory conjecture in order to allow the possibility of the existence of solutions without horizons because in this case there are no naked singularities of heights the possibility of existence of ultra-compact naked objects but of course we have been studying the problem of static spherically cementing black holes and obviously oversimplifying the scenario because real black holes in the universe do rotate so in order to see whether this feature for the black hole and this feature of the no singularity of the black holes is real or not in the mathematical point of view we need to obtain the analog solution with rotation and then again make all these things all these tests this is something we are doing a very difficult problem in order to obtain an analytical solution for this same setup with rotation we are working on making some large promises so maybe for the end of this year this will be ready so the final message of this talk is that the geometrical approaches beyond general relativity maintaining the same core principles that you have in your relativity say equivalence principle repetition manifestation of a curious space time so we maintain the same principles just staying the actual the thing, the law or the physical object that you have in your theory and when you apply these to objects like black holes or the very early universe you find that you can avoid space-time similarities in both the early cosmology and in the black holes these theories have also other particular interesting properties from the point of view as toxic cosmologies this work deals with some of these models and the final message of this talk is that there is a great importance of the use of multi-messenger geostronomy years to come in order to discriminate between different theories of gravity that are able to be whose compact objects will be able to be compatible with the observation of gravitational waves just with different masses and spins of the corresponding objects so it's necessary to gather both the theoretical knowledge that can come from the manifestation of gravity particularly those that are underlined here and those observations that we can make with compact objects from using gravitational waves so that's everything thank you very much for your attention so for any questions I will be thank you Diego for this nice talk let me see if we have something in the YouTube channel I believe we have one question from Shadu Xia sorry if I didn't pronounce that Diego you can go and if you want you can see in the YouTube sorry google hack out I shared the question so maybe you want to read it ok so that energy cosmology which is the oldest black hole discovered by humans that matter I'm going to ask you behind it I actually don't understand very well the question yeah it's just asking by chance you know which is the oldest black hole we have seen well I'm not very aware of the details about which is it probably he's talking about additional lensing from a black hole depending on that matter I don't know if he's asking about this thing because actually a way of testing the deviation from the vulnerability precisely using black holes black holes can capture these photons that travel around the black hole particularly around the inner muscular orbit they can turn around the black hole several times before being released and going back to alighting to some observer to show that the optical properties of these photons avail the physical features of the black hole that have captured them particularly in the case of in case of in case of gravity also the alighting in case of a way of testing the availability of these solutions okay thank you if you and you can stop sharing the screen so we can see you okay so I do have a question which is can you please comment a little bit on the stability of those wormholes when you actually studying the stability of black holes is a very pretty point so what we did was to study stability against tensorial perturbations actually there is a problem in particular features of these theories so I said there are two set of metrics there is a space-time metric and there is another metric I call Oceary so it turns out that for this part of black holes there are waves so the space-time metric is the physical object path there has been so many papers that the Oceary metric actually is the one that gravitational waves see right stability against tensorial perturbations of these solutions so you have to study the behavior of these waves of this Oceary metric and then there comes a problem because as you saw some of these solutions with black holes and with the early universe there can be instabilities in the sense that there can be growing modes that gets amplified so even if your solution is okay as soon as you consider the picture you quickly get the stone so this is a first test important test for the stability of both black hole solutions and corrobital solutions passing by this is compatible despite gravitational waves providing one different metric this is compatible because gravitational waves observations because the difference between these two metrics happens in environments of high energy density but in the wide range of propagation of the speed of light and the speed of gravitational waves therefore, gravitational waves impact the impact of these two metrics in the matter field so the impact of these metrics is considered to be compatible with gravitational waves observations because of this but the potential of stability of this Oceary metric might put it in the theoretical way of my ability okay, thank you so yeah, it was nice in your talk because some people think I believe that modifying general relativity is like you just have a huge back and then you start pulling theories and then you just make calculations but in fact it's very hard because especially what you mentioned during your talk which is it must first pass all the plethora of experiments so it's actually very hard to test a proposing modifications actually what you think on this there are many theories that are past-experimental solar system experiments and then many of these models as I said they are proposed as viable alternatives to cosmological model in the sense that might be statistically as significant as they land the city of Aurora so what's funny about this which we mentioned in astronomy is that a single observation of the snow waves it has been able to roll out many theories of gravity that are perfectly fine from the point of view of cosmology but they are not fine from the point of astrophysics so my hope is that in the near future as we are accumulating more and more and in the future thousands of observational observational waves from combat objects we will be able to put to experimental diet an experimental test many of these theories are being reached away that are consistent with the sport okay thank you do we have any other question from the law of physics coordinators? I have one question for Diego first of all it's very interesting to talk all the effort that are around in the area to see this difference between general relativity and the modification I have a couple of questions in the sense because many in these theories when they study black holes sometimes they include also the case when the black hole is charged is this also it's been in black holes that you mentioned at the end and you concluded that this is your working product but if you have any comments about what happened when in this context the black hole gets charged actually the solution the solution I was presenting was actually the charged solution and the reason because of this is because if you consider the counterpart of the vacuum Schwarz's solution this is exactly the same solution in general relativity and the reason is because the new collections that appear around this theory to general relativity solution are mediated by the matter fields there are no matter fields and Schwarz's are vacuum solutions or the solution is the same as Schwarz's in general relativity this theory is Schwarz's solution in general relativity so we have included the charts in order to obtain the variation of Schwarz's in general relativity solution now for the related solution because of the same reason as Schwarz's in one the care solution of these theories is exactly the same as the one in general relativity so in order to obtain the variations you need to consider the care and human solutions now we know that for astrophysical purposes the charge is completely negligible because the spin and the matter dominates overwhelmingly the contribution of the charge from the point of theoretical point of view black holes are completely discharged because many different reasons so they always retain a tiny amount of charge that can be negligible for astrophysical processes but it's not negligible at all or on the point of view of a physical extractor and the mathematical properties of this black hole potentially depending on where it comes from indeed we have verified a very tiny amount of charge it's able to produce dark changes in the structural research so because of these we are very motivated to find the counter part of the care and human solution as I said it's very difficult to do but recently this year we released a paper because the structure of this equation resembled so much that in our relativity all the matter on the right hand side we are attempting to compare the equation with general relativity and to find a potential correspondence between the solution of general relativity and the solution of this theory exactly what we found this theory I didn't mention in the talk there is a map that tells you how map and no solution of general relativity to that of one of these theories using purely algebraic affirmations instead of solving different elements which is the biggest challenge when we try to find a solution on this this is very important because when you try to do this in a way of astronomy using black holes there are many groups around the world which well developed mathematical and particularly computational method that are very strongly tied to the particular sculptor of the Einstein field equation and these methods are very difficult to translate to the case of these theories not because of the existence of this map that way is not needed what you need is just to find a particular scenario in the case of while this method you find theories say the permanent solution when you find the correspondence with the general relativity solution then you have to solve the Einstein equation into this you find the correspondence solution of general relativity using this map and then map it into the one of molecular particle this way you can use the full power of the computational methods developed in the contextual sphere and apply it directly to this theory sorry I have a second one second question thank you for the answers but the second question was related with in this kind of modified theories is there a better chance for instance to study effects related with quantum gravity or to coins put together particle physics in this metric background the stuff that is usually harder to do in general relativity because the theory explodes from the point of view of quantum mechanics or is there also approaches to try to make it smooth the transition between quantum and gravity in the sense yeah well I didn't mention anything about quantum gravity motivations because just if you have some comment we are seeing a classical approach in the sense we are including all these new invariance into the action this classical invariance motivated by the quantum theory by the theory in quantum physics that tells you that general relativity has to be supplemented by additional terms and we just kept ourselves at the quadratic level for the field equations we didn't go further we didn't even claim about where the scale present in this theory comes from so this elapsing of the theory could be plans scale or could be something completely different actually we are more inclined to see something completely different because our approach instead of using quantum gravity we use we try to think the basic principles that build general relativity the same what is the physical play by different mathematical structure I mentioned about the connection actually they are independent general relativity is just that because of the structure of the Einstein-Hebert-Grantzian the metric formulation is completely equivalent but because of the way that historically general relativity has been thought usually people assume that net rate approach is the only approach and then you supplement the action with new terms assuming that the connection is the levity but if you recognize the physical role of these quantities you have the independent material connection so you build up with these things and they are even more the very supreme in the sense that the connection we usually I didn't mention explicitly we assume that the connection is symmetrical actually the connection has a non-symmetric part just torsion torsion is usually neglected on the field equations because as long as you don't couple speeds or play no role but actually both torsion and the fact that they are not compatible that introduces another object which is number specifically contain new scales associated to them that are not planned scales and they are much below the energy that is expected to be planned scale so the fact that there are important geometrical elements that are appearing in my side maybe you are overlooking something so some key elements that are needed to understand how the another object could be extended without entering into the realm of quantum gravity where we have no much clues about what would happen there but I don't know if I I didn't assume completely under the form you were mentioning but it was very clear ok thank you Diego and thank you everyone for watching this webinar remember that this happens more or less every two weeks and now we have also introduced a colloquium I think that's the name we chose Roberto you can also see all this information on our web page or the youtube channel so thank you Diego thank you everybody and stay tuned for more webinars thank you very much for the invitation