Well, nice to meet you, folks. If only you actually said I wouldn't tell you about classical in quantum black holes.
It's an incredibly exciting subject. And so let me get started.
So black holes. Of course, one of the most awe inspiring objects in the universe.
They imply the end of spacetime as we know it. And also appear to imply deep paradoxes.
When we try to meld quantum mechanics with gravitation in particular, it's by context.
And as I said, there's actually, in fact, been significant progress, both observational and theoretical, in black hole physics in the past four years.
I want to tell you about these exciting developments.
And my message is going to be that the black holes should be thought of as like the hydrogen atom, the 21st century.
By studying this particular system, I think we can learn a great deal about what quantum gravity is.
And in fact, about other subjects, too. For instance, information theory and how it very surprisingly might connect with gravity.
So let me get started. So let me tell you a little bit about classical black holes.
So we now know that astrophysical black holes exist and behave to a very good
approximation the way that Einstein classical generals who he said they should.
And at least the exterior, we should emphasise that we only have information about the exterior of.
So Carswell Schwarzschild in 1915 was the first person who wrote down actually immediately after Einstein's general theory relativity appeared,
he wrote, and the first solution and the solution, in fact, was the black hole solution.
Sadly, while fighting and dying were war one. And so his solution has a property that has an event horizon, a black hole event horizon,
not that they realised really was property at the time, but it's there.
And his solution and a crucial aspect of what I will tell you about later.
And I hope you can see my point here is that the size of the black hole, the short shield radius,
the radius of event horizon is twice Newton's constant times the black hole mass oversea square.
OK, so this property. So I want you to remember that the short, short rate is the size.
The event horizon goes linearly with a black hole mass.
And so to give you an idea about what this says, Schwarzschild radius is for various objects for a solar mass,
black hole, short radius is just under three kilometres.
So if he crushed adiabatic lee the sun down to two point nine two kilometres, it would go inside its event horizon and form a black hole.
Instantly, if we maintained a constant distance from the sun, so we stay here on the earth, our current distance away from the sun,
and we did this idea that it crash crushing the force of gravity here on earth that we feel from the sun wouldn't change.
It's not like suddenly the black hole will strength. It causes gravity to come much stronger.
The reason why the strength of gravity is so much stronger at the black hole event horizon is just
because we concentrated a tremendous amount of mass and energy in a very tiny volume indeed.
And it's because we can approach much more closely.
So, of course, usually when we go to the sun, you're going to get close to the sun as the surface of the sun.
But here we crush it down to three kilometres. And that's the reason why the gravitational affective of a black hole is much larger.
It's because we are concentrating it so much. So anyway, that was a solar mass black hole.
We also know there exist supermassive black holes in the centre of almost all galaxies.
And these have masses somewhere between the range of ten to the six to 10 to the nine solar masses.
And therefore, correspondingly, they have a size which is quite large.
They have sizes which have older tend to the six to 10 to the nine kilometres.
And so, for instance, if you fell in into a galactic centre, supermassive black hole, you don't immediately die as you cross the event horizon.
Actually, you don't notice anything particular happening to you.
In fact, it takes you quite a few minutes until you reach the singularity and finally die.
So you can live. So an observer, according to our current theories,
understanding black holes can live for quite a long time inside a black hole and could make measurements.
So it's interesting question to ask. What would such an observer see?
And maybe we can discuss that later on in the question, not secessions.
We can also consider a hypothetical Blackhall investment earth mass,
and if you crush us into a black hole, it would have size just under one centimetre.
So this gives you an idea of the sizes of some possible black holes actually physically realised and possible hypothetical ones.
So what does the solution look like in equations? Well, we're talking about General Hibito.
You have to talk about the spacetime distances. Nature, geometry.
So here we have the S squared is a spacetime distance between events.
And this is given by this expression involves four coordinates. Two of them are just the normal angular corners D, Theta, Theta and Phi.
And this is just saying that everywhere there's a normal one. Spherical behaviour circle, symmetry, behaviour of the system where.
That's the area of a given sphere is four pi R-squared.
So this is this here. But now we have this issue here where we have this second term here gives you the fact that as you approach she horizon,
this denominator here is going to zero. So this factor here, there's an infinity that's appearing here at Times Square.
And this is telling you you get radial length contraction as the Iraq horizon is approach.
The other hand, this first term here, this factor, this is also going to zero as you approach to RSS, I guess you go to we will see Horizon.
This is saying that according to a static external observer, right far away from the black hole,
that as time dilation, as the horizon at a shorter radius of approach.
Right. So so there's both time dilation and radial length contraction.
Mr. Secretary. Well, that's in equations. And of course, you can study this.
Great, Lena. I want to emphasise that the more longstanding of classical black holes is due to record a number of people.
Wheeler, who coined the name Black Holes,
which will see libraries as somewhat inappropriate name and thanks Kruskal occur Thone Hawking and especially our own Roger Penrose.
And I think Roger made the greatest contributions to modern sounding of classical my calls.
So what are these awe inspiring objects look like? Well, here they are.
Here's a lovely little Etsy baby black hole. You can purchase for the low, low price of just 10 pounds.
Here's a baby black hole accretion disc for astrophysical black holes have accretion discs.
You can get these things with adoption certificates. That's lovely. Here is a different picture of what a black hole looks like.
We can take this geometry. And of course, it's very hard for me to represent the geometry of this situation in two dimensions.
But let me try. So this is a picture of radius and time.
He? S each of these points you should think of as a particular four dimensional thing,
as a as a two sphere sort of living about every one of these things.
And what I want, I emphasise is as this is the exterior. This white region is the exterior geometry of the black hole.
And then we have this horizon.
And the crucial thing is as you go inside your eyes and in fact, Space-Time itself is not really static inside the horizon.
The reason is, is because you don't get a hint of this from this thing as you go are is less than our.
Notice that this term here changes sign. And this thing here changes sign.
So that means now there is an overall negative sign in front of the R-squared and there is no real positive sign in front of the D.T. squared.
And that means this now becomes a spatial like coordinate. And this is the temporal called note here.
So, in fact, there's a definite different a Kornet system where you see this having better.
But you get a hint about what's going on here. And the idea is that, in fact, the radio corner becomes a temporal coordinate.
So, in fact, as you're going on with this thing, in fact, space time itself is dynamical here.
And is dragging you towards the singularity as you go down.
So as you see this picture being animated here. Well, as I emphasised before passing the horizon, nothing special happens to you.
There's no infinite forces. You don't necessarily get ripped apart.
The horizon of freely falling observer just thinks the horizon is very much like empty Minkowski space.
In fact, the only place where something truly singular and terrible happens to you is here, right at the singularity are equal zero in these corners.
But we should be wary about this because in fact, the classical solution.
And in fact, Einstein's classical generals, hefty itself is not reliable here.
So I want to emphasise to you that you that even though the singularity is predicted by classical general relativity,
we know the theory is not really self-consistent here.
So we believe that itself consistently describes exterior geometry and near the horizon.
But once we start approaching the singularity, we don't know what that physics is.
So, of course, the subject of active research I'm trying to understand. So here's another picture of what a black hole looks like.
And so here we have radius again. So here is a star collapsing to form a black hole.
And here we have an event horizon forming. And so the crucial thing about the event horizon is here.
Here is drawn are light cones. So this.
So what happens is light rise, quote unquote, ingoing or outgoing light rays have to be there on the edge of this light cone here.
And material objects, massive objects always travel less than the speed of light.
So I always have to travel with inside the light cone. So signals can only be sent in in these angles here.
So this one here is ingoing light. Right. And would go into the.
We go back into the black hole. But this one here would escape to infinity.
But there's this distortion of space time in the black hole background.
And what happens is the light cones tip over.
So once you go to the event horizon, now you see right at the event horizon, the outgoing light rays actually go right along the horizon.
All material objects inevitably go get dragged into the singularity.
That's the only possibility. And ingoing light rays, of course, go very quickly.
So it's this tipping over the light cones force you to go to the singularity is another way of saying that inside the event horizon,
forward in time becomes radially inward.
All right. So that's the thing.
But there's another thing here, which is, again, a freely falling observer, a freely falling observer going through this system.
I mean, we'll go through the rent rising, hit the singularity. But nothing special happens is really falling observer.
She through force, through the horizon. It's just the usual finite tidal forces.
You always get when you're in the external gravitational fields.
All right. So there will be tidal forces on this person who is a tiny black hole.
These tidal forces might be strong enough to rip the person apart, spike spaghetti for her.
But otherwise, it's a large black hole like a galactic centre, black hole falling through horizon of such an object gain.
Nothing special happens in the observable survive. A human would survive.
And only when you finally get to the singularity, which should be destroyed.
And so I emphasise, if we go back to the metric,
it looked like there was apparently singular behaviour in this metric near our equals, our s, and that's why.
And in fact, took roughly 45 years or so before people took black hole solutions seriously, they thought.
In fact, this wasn't sensible. This only could be used as if it was a mathematical artefact.
But later on, it was realised. In fact, there's nothing singular about this solution apart from right at the Singularity Arkos zero.
In fact, this apparent singular behaviour, the short geometric, is just a natural supporters.
It's like longitude. If you're at the north and south poles, it's a corner that breaks down.
It's not truly physics breaks down at the event horizon. So that was that.
Now. We now know to a very, very high degree of confidence that supermassive astroparticle black holes exist in galactic centres of most galaxies.
And so here is a little movie, which I hope now plays.
So this is pointing towards our galactic centre and it's starting over a whole bunch of years, the motion of the stars.
And what you see here is a right at the galactic centre.
This is a tiny distance, 10 light days that the stars are orbiting around a very massive, very centrally concentrated object.
In fact, there was a Nobel prise shared with Roger Penrose this year in 2020,
where these two teams, led by these two investigators, independently show.
By measuring the trajectories of these seven stars. Right. Close to the likely centre.
They're not they're not perfectly on ellipses.
In fact, there are general relativistic effects exactly of the kind predicted by General 50 in the background of a black hole.
The slight distorting these lipsett. So this is a confirmation.
You have a supermassive black hole with a guy with a very high degree of confidence at our collective centre.
So recently we have a direct image of a supermassive black hole, not in our galaxy fate in M80 seven.
This is from the Event Horizon Telescope in 2019. And here is the shadow, the event horizon.
And here is the accretion disk. So just like that little Etsy toy you can buy here.
What the light is coming from the accretion disk is the black hole. And here is the shadow of the event horizon.
So we now know there's a whole range of black holes. And in fact, we have another way of looking at black holes, not just visibly,
but we also now here in the sense the sound of black holes merging through gravitational waves.
So, again, I hope you can just click on this thing. Sometimes it's worth.
Do you hear that sound, doesn't hear the sound? I hope so.
It's so that is the sound. It was picked up in the gravitational wave detectors,
the advanced liger collaboration that they have two sell at Hanford and Livingston in the United States.
And this is the sound, the final chirp as the two black holes, two very supermassive black hole, actually, not supermassive.
Very massive. Multiple solar masses are rotating together and finally colliding and they merge.
And during that final seconds there,
the energy released in gravitational waves far exceeds the energy produced by all the suns in all the galaxies in the universe.
It's an extraordinary three or four solar masses worth of mass are being converted to energy, almost alling and gravitational waves.
And so now we've seen dozens, actually hundreds of black hole mergers.
And so this is merger tree of how black holes of urging, merging and evolving.
And of course, it's nice. Let's see thing.
And the nice thing about this is let's see cartoon you see here is, in fact, it shows these two black holes will be rotating around to each other.
The final black hole produces a highly spinning black hole. So it's not a short, tall black hole, but the astroparticle black holes.
We have a highly rotating just for simplicity in this Coke. I'm going to focus just on short term black holes, non rotating black holes.
Okay. So the summary is, is we know there's a wide variety of black holes exist in our universe.
And they're very well described by Einstein's by this virtual solution or the curse solution.
It's generalised the rotating generalisation in external region.
So my interest, though, is quantum black holes.
That's what I want to tell you about. So the classical theory of black holes is extraordinarily rich.
But the world is really quantum mechanical. And so we need to study what the behaviour of quantum mechanics, what a quantum behaviour, black holes is.
And what we are going to find is even more remarkable in the classical case.
And it apparently leads to deep paradoxes and these deep, dark paradoxes, rather like the birth of the early history of quantum mechanics itself.
The thinking about these paradoxes and understanding how they're resolved is
guiding us towards a much better understanding of aspects of quantum gravity.
So I would emphasise it's been significant progress in the last years, and I will tell you a little bit about what the significant progress is.
All right. Next slide. So the first thing to realise is the most basic quantum facts about a black hole is hawking radiation.
So let me tell you about why what hawking radiation is and why it exists.
So in relativistic quantum mechanics, sometimes we call quantum field theory empty space, quote unquote.
The vacuum is full of quantum fluctuations of all fields and particles.
So it's not a static. You shouldn't really think it is an empty thing. So here is actually a precision numerical evaluation of the vacuum of QC day.
This is on a five Fermi cubed lattice.
And this is a a time loop of it. And here we just have one realisation show we spoke to Super posed a different
quantum superposition and we have different positions of what the vacuum is doing.
This is one realisation. And you see this thing is fluctuating like crazy.
We're getting fluctuations of scales that you see.
There's a typical sort of scale here that set by the scale of QCT, its self, which is Voda itself about one Fermi.
Right. Or 200. I mean, the Lambda QCT. So.
And instantly this is verified, these cutey deep precision calculations.
And now give you quite accurate description of the low lying masons and baritones and various other states, other properties.
We know this is true. We know quantum motivations are there for many reasons. This is one demonstration.
So what about hawking radiation? Well, so here we have space time and here's a black hole.
And as I emphasised, at least near the horizon, it's just like empty Minkowski space.
So we have these positive and negative energy, virtual particle fluctuations happening everywhere.
We have them happening outside the black hole. We have them happening certainly in the region anterior to the black hole.
As long as we're not very close to the singularity, we don't know what's going on.
Singularity, but certainly in the region around the horizon, we have these virtual particle fluctuations.
I won't ever size the particles antiparticles here, but is the crucial thing is whether they're positive or negative energy overall.
These things have zero energy. All right. And there is a correlation between their energies such.
They start off in the vacuum, go back to the vacuum, constantly doing this.
Well, if you have one of these fluctuations in the vicinity of the rise in the black hole,
there's a quantum mechanical tunnelling process that allows the positive energy guy here in red, which could be a particle or an antiparticle.
So I don't know, you'd get confused. It's not always that particles come out of the black and antiparticles go in.
It can be either particles or antiparticles can escape. The crucial thing is whether they're positive energy or not.
So rarely is tunnelling process allows a positive energy particle or antiparticle to a state to infinity while its negative energy sibling.
And this is negative energy from the perspective of some distant observer particle or antiparticle is captured by the black hole.
And therefore, because it's negative, energy reduces the black hole mass. So the end effect of this is the black hole.
Mass has gone down slightly and its energy has been radiated away to infinity a little bit.
And I like to experts here, this is sort of sometimes given as an intuitive picture of hawking radiation,
that this tunnelling picture of organisation can be made precise.
And he has an interesting advantage over Hawking's original calculation that actually explicitly shows the black hole mass is reducing.
In fact, in Hawking's calculation on deficit of it maybe is that it's on a static background where the
black hole mass is not reducing these tunnelling way of thinking about hawking radiation. In fact,
shows the black hole mass is being reduced and its it is being reduced by this sort of inflow of negative energy from the distant observers suspect.
So the end result of this is physical black holes are never truly black.
In fact, they produce thermal radiation, all climatically allowed modes.
And here is a little cartoon. So I went inside dominantly for black holes. It would be gravitons, photons or maybe neutrinos.
But in fact, in fact, all kinematics available modes are allowed. So amazing.
End result is black.
Was a thermal system with a temperature gain is seen by a far away static observer t hawking and the hawking temperature here it is goes like h bar.
It's a quantum effect. C cubed over eight pi. Newton's constant.
K Boltzmann. If we want normal temperature, normal kelvin units and then one over the massive black hole we put in for instance a massive black on KG.
Imagine we had a kg sized black hole. That's a logically consistent thing to consider though.
Hypothetical, and since we've never observed such a thing, it would actually have a very high temperature.
Ten to twenty three, Kelvin. So it's not like this is a small temperature, at least if we have a small black hole.
This is a very large temperature for a small black hole.
On the other hand, because astrophysical black holes are so massive, solar mass for solar mass.
My call. It's ten to the minus seven Kelvin. So that means that we're never going to observe, at least for astrophysical black holes.
The Hawking temperature satellite.
But if you start off with a black hole, let's say you start a full black hole, which is in between a kilogram and a solar mass.
Well, it would start radiating energy. It was mass will work with we all juice and therefore its temperature will rise.
And there's a runaway process here. So that's important to bear in mind.
I want you to remember that for Lytro. So Blackhall Hawking radiation has never been observed.
But we have a high degree of confidence. That's true. We now know many ways it could be theoretically derived.
And it solves some otherwise troubling aspects of classical black hole physics.
Let me tell you a little bit by one of these quite troubling aspects.
So one of these is associated with a second law of thermodynamics, which, of course, is that the change in entropy,
in a physical process should be greater than zero or equal reserve if it's reversible.
So Fleckenstein argued that to say the second law one must sign and I want to emphasise is a finite end to black holes.
Otherwise, one could systematically reduce the entropy of the universe by throwing in matter with entropy greater than zero, which then disappears.
All right. And if you do not assign any entropy to the black hole, then you reduce systematically the entropy of the universe.
By doing this process, by just quantity recycling this process, you could use it with universe.
This is a pretty bad thing. So Berenstein suggested, in fact, that the entropy of a black hole is fine.
Entropy should be proportional to the area.
The black hole and Hawking's calculation of the temperature confirm this because the first laws were seven.
Amik says d e equals temperature times D.
S with the E is the change in the energy. The S is the change in the entropy.
And we now have a formula for the temperature due to Hawking and we know the energy.
Here is the massive black hole time C squared. And if you put this N, you put the formula in for your tea.
Hawking arrived earlier and you put in what you just take the derivative.
This thing, d.A. So it's just the M C squared. You can then find what the change of D.
S is D. S and integrate that up. And what you find is you find this expression for the entropy of a black hole.
It goes. This is called the either the black hole entropy or the Berenstein Hawking entropy.
It goes like CS cubed on G Newton one over H bar.
And then the area, the black hole on four.
In fact, this combination of units here, this defines the planked length squared or the one over the Planck link squared.
Another better way of writing this is one quarter of IE.
The area of the black hole event horizon over the Planck Link Square.
I want out I want you to notice this Planck length squared is Planck length is incredibly tiny,
is approximately ten to the minus 33 centimetres and black.
Oh, of course. Black hole of enterprises. Well, that macroscopic things there.
You know, kilometres squared or much bigger banks.
All right. Or much bigger for supermassive black holes.
Now, I want to emphasise to you that here. Notice isn't one over H bar here.
So that means the classical limit. Each bar goes to zero. The entropy of a black hole in the classical limit will be infinite.
And this is why you can constantly keep highlighting entropy there in this process. Why should you?
Homer Simpson falling into a black hole. So this should remind you of the catastrophe of plis pre plank classical black body radiation spectrum.
The fact that the quantum effects actually make finite insensible what will be an infinity in the classical theory.
That's very interesting. So that's one way of thinking about this.
Well, one way of thinking about the meaning of this entropic formula that the entropy goes like one quarter.
The area over Delplanque squared is as one cubitt sorry, one cubic per for Planck areas for the arisan.
So here is the event rising, divided up in little things.
And there's a cubit, you know, either zero one basically on average, one for every two or four triangles or Planck areas here.
So this is a very, very rich and complicated system, has an enormous number of cubits.
Let me tell you about that. Well, the entropy if you put in this formula for a solar mass black hole,
you find the entropy is a vote would attend to the 77 times the mass of the black hole over M Solar Square.
That means the entropy of a single solar mass black hole is roughly equal to that of the entropy of all the stars in the entire universe.
In fact, because these guys like mass squared and we know there exist supermassive black holes,
the entropy of a super a single supermassive black hole exceeds the entropy of everything else in the universe.
So that's an extraordinary statement.
Another way of thinking about this very large entropy is quantum black holes of thermal systems with a huge number of microstates member.
If we take member Boltzmann's famous Formula S is.
Well, let's forget in place of constant Essy was log W with W's number of microstates.
The system, which says high then exponentially therefore misses a number of states,
is approximately exponential of this century and this century is already huge.
So the number of states of a black hole, a low lying state, so black hole is incredibly large.
It's bigger than Google, vastly bigger than a Google.
So this has some comments. Well, the information content of the universe appears to be hugely dominated by black holes.
That's a remarkable statement. We don't understand well, these microstates of black holes, exactly what these microstates are.
There's some progress in string theory, but aren't sending is certainly not complete.
Very interesting. Late this Entropia respected site hawking entropy or the black hole.
Entropy is not extensive. It goes with area, not volume.
It doesn't go with mass either. Goes like mass squared because it area.
This leads the idea of the holographic principle which motivates mouther signer's actually
very specific and concrete thing called A.D.s CFT duality for certain space times.
So this holographic principle says basically that the infinite information content of a region goes like the area,
the bounds the region rather than the region itself. So there's far less degrees of freedom than you might think in in a theory.
This is an incredibly rich area that deserves an entire morning in itself.
I don't have a size that we understand holography reasonably well, inequitably curved space time.
We don't understand Flatt's white space a lot graphy currently.
So that's already something remark. We got out of black holes. But let me turn to some other implications for creation.
Well, since hawking temperature increases and decreases black holes and explosively evaporate
by runaway hawking radiation and the end temperature of hawking evaporation,
a black hole is almost planking is incredibly high temperature.
So this means that hawking reparation is quite extraordinary.
Every particle in nature with mass less than implant overwrite pi.
So that's about 10 to the 18 G.V. can be produced even if it's completely decoupled from the standard model.
And the reason is nothing. Hisam gravity. This is not using evaporation.
Occupation doesn't depend upon a particle being charged or colour charge or anything like that.
Having company Salmo nothing hisam gravity.
Therefore Hawking evaporation is a scan over all of creation, even things that are hidden from the standard model.
So this way you can produce, for instance, dark matter or even start a hot phase of the big bang.
And so I've been investigating these issues with my students.
These are three of my very good graduate students here at Oxford and Olivier Rudan and Hannah.
Two of them, I think, are in some of the breakout sessions. We have to talk, too.
So this leads to what could be observable signatures and hawking radiation, hiding in dark matter and in gravitational waves.
Adam, very sadly and of course, whole Steven himself.
We've got see this. But if we'd seen Hawking radiation, he would have been able to win his very well-deserved Nobel prise.
So this is quite incredible. Why was Ms. I'm surprised. Yes, there's this possible observable signatures hawking radiation, but there's more.
Right. Adam, coking evaporation applies a remarkable consequence that many for the theory, including gravity,
there are non spies and non spacetime global symmetries or with violated this approximate at best.
So let me just quickly describe this mean what this means.
This means you can't have exactly to generate physically distinct states without him such internal symmetries.
You can't have an exact quote. Zack Clay. Every potential surface.
Let me just explain why this is true. Well, we know Emmi Novia taught us that if you have a symmetry, you have global challenges.
So if you if you slightly violate this symmetry, that means the global charges are not conserved.
So one example of this would be the non conservation of barrier number, for instance,
snapping not normal Yousafzai Baren number with some you won global symmetry with this must be violated.
So here's the argument of why it's true. Go back to Zelda, which so imagine you start forming a black out of a large initial number of neutrons.
So you crush these neutrons to form a black hole,
but then it hawking evaporates and is hawking radiation is independent of whether your initial state is a barrier on the balance or anti baryonic.
It only cares about the mass spin in charge of these states, not whether they're baren anti barium.
So at most the final state has plus or minus root end of of Barry on charge here.
The blue there's one, the three blue and one reds is one net state.
Here we started out with a lot. So you lose Barry a number in this process.
So global symmetries are violated by hawking evaporation.
Now, there's a we don't extend exactly how this works.
And for generations in particular, we don't sign a form and summarise the global symmetry value interactions.
But there's progress, again, by by groups involving me,
but other people as well around the world and progress, recent progress being made on this issue.
That's interesting. So I'm almost done. Let me make a few final words.
So one issue I haven't spoken about is if quantum mechanics and black holes are, in fact inconsistent with each other.
And this was the view of Stephen Hawking himself for many years, though I would say not for the last five years, his life might still be Roger.
Roger Penrose is you. So what is the reason for this?
Well, hawking evaporation of black holes appears to allow for quantum mechanical, pure states to evolve to mixed states.
If so, this would be of would violate a fundamental axiom of quantum mechanics and imply information loss.
But in the last two years, there's been major progress on this issue and a consistent calculational framework is now emerging.
So there's a whole bunch of papers from people for the Institute of Arts today, from Stanford, from M.I.T., from other places as well.
And what is their basic idea? Notice that some very exciting things here, replica wormholes in the black hole interior.
This is trying to understand in a real way what is the physics of the interior?
What observers who fall through the arisan would sees is crucial in understanding these issues.
And you're having some very interesting things like wormholes appear, other kinds of solutions possibly to Einstein's equations.
So the basic idea, and this is true for experts, is that Hawking's calculation of this thermal effect is thermal density matrix was never exact.
In fact, we always knew that it had his calculation had loop effects there.
But in fact, the paradox was, is all these local quantum field theory loop corrections don't help solve the paradox.
It turns out you can show. But now it's been realised. There are new tiny non perturb two effects, which are Suckley non-local.
All right. And that's the crucial thing. They're very tiny. They go like E to the minus area, the black hole over Delplanque Square.
They're incredibly tiny.
So you may say, how can these incredibly tiny effects make a difference and somehow change mixed states, what looks like a mixed state or pure state?
And the answer is, if you compute the radiation, the entropy of the radiation is coming out.
So some other states of the eigenvalues of this density matrix and these eigenvalues
now shifted by exponentially small amounts because of these tiny corrections.
But there's an exponentially large number of states here.
Remember, emphasised before that the black hole was an he let excellent large number of states.
So there's exponentially larger number of terms times, exponentially small corrections to each one of these terms.
And this can lead to an order, one modification. And in fact, there are demonstrations in simple cases that this purifies the final radiation.
So leads to pure state to pure state evolution, meaning that quantum mechanics is consistent with black holes.
So I want to finish there with a statement, the quantum mechanics, black holes is even more remarkable than you might have thought.
He's guiding us towards a better understanding of quantum gravity, and I emphasise information as well.
And so I think is very good reason to believe that black holes are quantum black holes.
And think about the hypernatremia 21st century. So I'll stop there.
Thank you.