The Information Paradox for Black Holes

0:00 Thank you. Thank you. Can you hear me? I want to report that I think that has solved a major problem in theoretical physics that has been around since I discovered that black hole slated internally 30 years ago. The question is, is information lost in black hole apparition? If it is, the apparition is non-unitary and pure quantum space decay into mixed space. On the other hand, if information is not lost, how it will disappear out of black hole?

2:30 The Black Pole information federalize started in 1967, when Murner Israel showed that the Schwarzschild battery, was the only static agnode black hole solution. This was in general as the Tanoe-Periturium, the only stationary rotating black hole solutions of the Einstein-Maxwell equations are the Tanoe-Noumen batteries. A no peridural implied at all information about the collapsing body, who was lost from the outside region, occurred from three concerned quantities, the mass, the angular momentum, and the electric charge. This loss of information wasn't a problem in the Classical Theory. A Classical Flexible would last forever, and the information could be thought of as preserved inside it, but just not fairly accessible. However, the situation changed when I discovered that quantum effects would cause a black pole to radiate at any rate. At least in the approximation I was using, the radiation from the black pole would be completely thermal and would carry no information. So one would have to throw that information locked inside a black hole and evaporate away and disappear completely. It seemed the only way the information could come out would be if the radiation was not exactly thermal, but had several correlations.

5:00 No one has allowed a mechanism to produce correlations, but most physicists believe one must exist. If information were lost in black holes, pure quantum states would decay into mixed states, and quantum gravity would be unitary. I think it's okay without the mic, actually. I first raised a question of information loss in 75, but the argument continued for years without any resolution in the way. Finally, it was claimed that the issue was settled in favor of conservation of information by ADS-CMT. ADS-CFT is a conjecture duality between supergravity and NET center space, and the conformal field theory on the boundary of NET center space at infinity. Since the conformal field theory is manifestly unitary, the argument is that supergravity And the information that falls in a black hole in MED center space must come out again. But it still wasn't clear how information could get out of a black hole. That is this question I will address.

7:30 Black hole formation and evaporation can be thought of as a scattering process. One sets in particles and radiation from infinity, and measures what comes back up to infinity. All measurements are made at infinity, where fields are weak, but one never probes the strong field region in the middle. So one can't be sure of that whole forms, no matter how certain it might be in classical theory. I shall show that this possibility allows information to be preserved until they return to infinity. I adopt the European approach, the only sane way to do one of gravity non-perturbity. In this, the time evolution of an initial state is given by a path integral over all positive definite letters that go between two surfaces at a distance t apart at infinity, one in which rotates the time integral, t, to the Lorentzian. Thank you.

10:00 is taken over metrics of all possible topologies that fit in between the surfaces. There is a trivial topology, the initial surface across the time interval. Then there are the non-trivial all the other possible topologies. The trivial topology can be foliated by a family of surfaces of constant time. The path integral neural metrics with the trivial topology can be treated canonically by time slicing. The one unit is the same as per the path integral for ordinary quantum fields in flat space. One divides the time interval into time steps, delta t in each time step, one makes a linear interpolation of the fields, and their conjugate momenta, between their values and successive time steps. This method applies equally well to topologically trivial quantum gravity, but shows at the time evolution, including gravity, will be generated by an amelotorium. This will give the unitary mapping from the initial surface to the final.

12:30 This argument cannot be applied to the non-trivial topologies. They cannot be correlated by a family of surfaces of constant time. There will be a fixed point in any time-evolution vector field on the non-trivial topology. A fixed point in the Euclidean regime corresponds to an horizon in the Lorentzian. A small change in the spin on the initial surface would propagate as a linear wave on the background of each metric in the path integral. If the background contained the horizon, the wave would follow through it, and would decay exponentially at late time outside the horizon. For example, correlation functions decay exponentially in black polar metrics. This is a heuristic argument in support of the plausible conjecture that the path in the global overall topologically nontrivial metrics will be independent of the state on the initial surface. It will not add a B amplitude to go from the initial state to the final state that comes from the path-indegor-over-all topologically trivial matrix. So, the mapping from the initial So the final space, given by the path integral over all metric, will be unitary. Further evidence for this conjecture will be given later.

15:00 One might question the use in this argument of the concept of a quantum state for the gravitational field on an initial or final space-like surface. The wave function for gravity is the function of the geometries of space-like surfaces on the matter fields. This is not something that can be measured in leaf fields near infinity. One can measure the weak gravitational fields on the time-light tube around the system, but the caps at the top and bottom go through the interior of the system where the fields may be struck. Thank you. getting rid of the difficulty sub-caps would be to join the final surface back to the initial surface and integrate over all spatial geometry sub-caps. If this was an identification under a Lorentzian time interval at infinity, it would introduce closed time-like curves. But if the interval at infinity is a Euclidean distance, beta, the path integral gives the position function for gravity at temperature, 1 over beta.

17:30 There is an infrared problem with this idea for asymptotically flat space. The partition function is infinite because the volume of space is infinite. it. This problem can be solved by adding a small limited cosological constant, which makes the effective volume of the space finite. It will not affect the evaporation of the It's a small black hole, but it will change infinity to MED center space and make the thermoplexation function finite. The boundary and infinity has apology as one cross has two. The simplest topology that fits inside that boundary is the trivial topology S1 X D3, the three disc. The next simplest topology, the first non-trivial topology, is S2 X D2. This is the topology of the Schwarzschild and the DeSinner metric. There are no possible topologies that fit inside the boundary, but these two are the important cases, topologically trivial metrics, and the black pole. The black hole is eternal that cannot become topologically trivial at late times.

20:00 In view of this, one can understand why information is preserved in topologically trivial metrics, but exponentially decays in topologically non-trivial metrics. A final state of empty space without a black hole would be topologically trivial, and be forwarded by surfaces of constant time. These would form a three-cycled module of the boundary and infinity. Any global symmetry would lead to conserved global charges on that three-cycle. This will prevent correlation functions from decaying exponentially in topologically trivial metrics. Indeed, one can regard the unitary Hamiltonian evolution of a topologically trivial metric as a conservation of information through a three-cycle. On the other hand, a non-trivial topology, like a black hole, will not have a final three-cycle. It will not therefore have any conserved quantity that will prevent correlation functions from exponentially decaying. It is therefore very possible that the late time amplitudes of the path integral over topologically non-trivial metric are independent of the initial state.

22:30 In a thought-provoking paper, might the center consider how the loss of information into black holes in ADS could be represented with the unitary of the CMT on the boundary of ADS. He studied the canonical ensemble for ADS at temperature 1 over beta. This is given by the patent law for all matters that fit inside the boundary S1 cross S2 where the radius of the S1 is beta times the radius of the S2. For small beta, there are three classical solutions that fit inside the boundary. They are, periodically identified ATS, a small black hole, and a giant black hole. If one normalizes a d-estimate zero action, small black holes have positive action, and giant black holes have very large negative action. They therefore dominate the canonical ensemble, but the other solutions are important. I'll descend and consider two point correlation functions in the CNT on the boundary of ADS. The expectation value of O of Y, O of X, can be thought of as the response at Y, to disturbances at X.

25:00 It would be difficult to compute in a strongly coupled CFT, but by ADS-CFT, it is given by boundary-to-boundary green functions on the ADS side, which can be computed easily. The green functions in the dominant giant black hole solution had the standard form for small separation between x and y. However, they decay exponentially as Y goes to late times, but most of the effect of the disturbance at X falls through the horizon of the black hole. This looks very much like information loss into the black hole. On the CFT side, it corresponds to screening of the correlation function, whereby the memory of the disturbance sags is washed up by repeated scattering. However, the CMT is unitary, so theoretically it must be possible to compute its evolution exactly and detect the disturbance at late times from the many-point correlation function. All green functions in the black pole matrix will decay exponentially to zero. However, my descendants realized that the green functions in periodically-identified ATS don't decay and have the right order of magnitude to be compatible with unitary.

27:30 In this paper, I have long further shown that the path integral moved topologically Equival metrics like periodically identified ATS, that's to the terrain. Giant black process table, but don't evaporate away to nothing. On the other hand, small black holes in ADS are unstable and behave like black holes in asymptotically flat space. One can eliminate the giant black holes by integrating the partition function, z of beta, along the contour parallel to the imaginary axis, with the factor e to the beta e0. This projects out the space with energy, e0. Then the gravitational collapse and evaporation, one is interested in states of definite energy rather than states of definite temperature. For small e0, most of the states will be thermal radiation in ADS, but occasionally, thermal fluctuations will lead to collapse to a small black hole. This will then evaporate again. A similar discussion of correlation functions on the boundary shows that the topologically trivial members may collect all formation and evaporation, unitary and information-preserving.

30:00 So, in the end, everyone was liked, in a way. The information is lost in top of logically non-trivial matters, like black holes. This corresponds to dissipation in which one loses sight of the exact state. On the other hand, information about the exact state is preserved in topologically trivial metrics. The confusion in paradox arose because people thought classically in terms of a single topology It was either a polar or a black pole. But the famous sum over histories allows it to be both at once. One cannot tell which topology contributed the observation any more than one can tell which slit the electron went through in the truthless experiment. All that observation at infinity can determine is that there is a unitary mapping from initial states to final, but that information is not lost. In this talk, I have learned you that quantum gravity is unitary, and that information is preserved in black hole formation and evaporation. I assume the evolution is given by the equilibrium path integral over matrix of all topologies. The integral over topological integral matrix can be done by dividing the time integral

32:30 into thin splices, but using a linear interpolation to metric in each splice. The indigo for each splice will be unitary, and so the whole path indigo will be unitary. On the other hand, the path integral that's opologically non-trivial metrics will lose information and will be asymptotically independent of its initial conditions. Thus the total path integral will be unitary, and quantum mechanics is safe. Thank you. My work with Myrtle showed the radiation could be thought of as tunneling out from inside the black pole. It was therefore not unreasonable to suppose that it could carry information out of the black pole. This explains how Black O can form, and then give out the information about what is inside it, while remaining on top of the line to be trivial. There is no way the universe branching off, as I once thought.

35:00 The information remains firmly in our universe. I am sorry to disappoint science fiction fans, but if information is preserved, there is no possibility of using black poles to travel to other universes. If you jump into a black pole, your mass energy will be returned to our universe, but in a which contains the information about when you were liked, but in a state where it cannot be easily recognized. There is a problem describing what happens, because strictly speaking, the only observables in quantum gravity are the values of the field at infinity. One cannot define the field at some point in the middle because there is quantum uncertainty in where the measuring is done. What is often done is to adopt a semi-massive approximation in which one assumes that there are light numbers and applied matter fields coupled to gravity. One neglects the gravitational fluctuations, because they are only one among end quantum loops. However, in ignoring quantum loops, one throws away unitary. A semi-classical metric is in a mixed state already.

37:30 The information loss corresponds to the classical relaxation of black holes, according to the known error. One cannot ask when the information gets out of the black hole, because that would require the use of a semi-classical metric, which has already lost the information. In 1997, before the night, then planned for school, that information was lost in black The Loser of Losers of the Met were to provide the winner of winners with an of their own choice, from which information can be recovered with ease. I conceded a bet, but Kev Thorne is convinced just yet. I gave John Pruskyo the encyclopedially requested. John is all American, so naturally he wanted an encyclopedia of baseball. I had great difficulty in finding one over here, so I offered him an encyclopedia of cricket. But John wouldn't be persuaded of the superiority of cricket. Fortunately, my assistant, Andrew Dunn, persuaded the publisher's sports classic books to fly out a copy of the most recent edition of Total Baseball, the ultimate baseball encyclopedia.

40:00 I gave John the encyclopedia. If Kip agrees to conceive of that later, he can pay me back. Thank you. Okay, so there's time for a few questions, and Stephen, there really needs to be questions in the yes-no. I remember that you asked me once, maybe about 20 years ago, he said that in 10 years, string theory resolved the problem of quantum gravity. I was going to ask if you still believe me. can you stand up so you made some comments about what was wrong with a semi-classical treatment but one can do in a fixed semi-classical treatment one can compute as you did the radiation coming out from the black hole for most of its life it would seem that that would be computation until you got near the end of the black hole. But if that's so, then information has not been preserved. So are you saying now that the semi-classical expressions for the radiation are wrong even when the black hole is very large and one would naively have thought that they were correct?

42:30 can you say what's wrong I think there's a way to actually preserve the semi-classical calculations perfectly fine and yet have information not lost and I would like to make a case I will actually make a case for this in my car so you can again ask a question at that time the question for Stephen was really But it seems to me that the argument is still at a conjectural level, and the key, the technical stone of this conjecture is how Green's functions behave in this non-strivial apology, which got started backwards. Now, if I did not focus on political concepts, people have worked out how the Green's functions of decay. And while there are some exponential fall-offs, there are also tail terms, which are only polynomially, basically, b to the minus 3, or u to the minus 3, when u is the retarded time. Now, there may well be very, the situation may be dramatically different in the case of anti-discipline, where there is a cosmological constant, and there may the actual exponential fall off. Is that what you are saying? I am asking just no questions. Thank you.

45:00 Sorry, those are all the questions. Colin? Can I think about the disconnected telemetry, to separate this space? And if the answer is yes, the second question is, can I think the transition altitude between having a sink, if you don't see it, and having a sphere with you? I guess this is the answer to the question, so that I can consider disconnect with geometry. And the answer is yes also to the fact that the initial activity between one and two is over the z. Thank you. Thank you.

47:30 Okay, any other questions? Well, this is a stupid question, but what if you engineer a black hole to never decay? You know, you put it in a box that reflects its stuff back, or you just keep throwing things into it, or whatever. have such possibilities already included in effect in the whole business of doing the math integral and so on, I mean, basically, I better have this so that yes and no I don't know if it is, it is that kind of thing okay, okay the idea of a cyclic universe is very popular now EMIO is actually used to constrain that because we can't destroy information during the bounce and it will accumulate and so somehow we need to erase, we need in effect to erase information from the previous universe if we had a cyclic universe one. Right, can we all extend it to the site of the universe? Thank you.

50:00 If I understood, you computed a kind of propagator or S-matrix or dollar matrix at infinity by a contribution of different topological sectors. And in the trivial sector, you said that the propagator would be unitary. But in the non-trivial sector, it sounded like everything would go to a single state, which is very far from unitary evolution. So are you somehow saying that add together those two propagators corresponding to the two different topologies, one with information loss and one without, that somehow the result is unitary. Okay, is there a last question? Ok, so I have a last question. So Stephen, are there topologies for which some information might be lost, are there some topologies for which only some information is lost? So I'll bring the proceedings to oppose and let's thank Steve again. Thank you.