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Well, nice to meet you, folks. If only you actually said I wouldn't tell you about classical in quantum black holes.

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It's an incredibly exciting subject. And so let me get started.

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So black holes. Of course, one of the most awe inspiring objects in the universe.

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They imply the end of spacetime as we know it. And also appear to imply deep paradoxes.

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When we try to meld quantum mechanics with gravitation in particular, it's by context.

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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.

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I want to tell you about these exciting developments.

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And my message is going to be that the black holes should be thought of as like the hydrogen atom, the 21st century.

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By studying this particular system, I think we can learn a great deal about what quantum gravity is.

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And in fact, about other subjects, too. For instance, information theory and how it very surprisingly might connect with gravity.

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So let me get started. So let me tell you a little bit about classical black holes.

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So we now know that astrophysical black holes exist and behave to a very good

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approximation the way that Einstein classical generals who he said they should.

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And at least the exterior, we should emphasise that we only have information about the exterior of.

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So Carswell Schwarzschild in 1915 was the first person who wrote down actually immediately after Einstein's general theory relativity appeared,

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he wrote, and the first solution and the solution, in fact, was the black hole solution.

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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,

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not that they realised really was property at the time, but it's there.

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And his solution and a crucial aspect of what I will tell you about later.

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And I hope you can see my point here is that the size of the black hole, the short shield radius,

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the radius of event horizon is twice Newton's constant times the black hole mass oversea square.

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OK, so this property. So I want you to remember that the short, short rate is the size.

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The event horizon goes linearly with a black hole mass.

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And so to give you an idea about what this says, Schwarzschild radius is for various objects for a solar mass,

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black hole, short radius is just under three kilometres.

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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.

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Instantly, if we maintained a constant distance from the sun, so we stay here on the earth, our current distance away from the sun,

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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.

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It's not like suddenly the black hole will strength. It causes gravity to come much stronger.

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The reason why the strength of gravity is so much stronger at the black hole event horizon is just

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because we concentrated a tremendous amount of mass and energy in a very tiny volume indeed.

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And it's because we can approach much more closely.

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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.

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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.

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It's because we are concentrating it so much. So anyway, that was a solar mass black hole.

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We also know there exist supermassive black holes in the centre of almost all galaxies.

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And these have masses somewhere between the range of ten to the six to 10 to the nine solar masses.

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And therefore, correspondingly, they have a size which is quite large.

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They have sizes which have older tend to the six to 10 to the nine kilometres.

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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.

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Actually, you don't notice anything particular happening to you.

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In fact, it takes you quite a few minutes until you reach the singularity and finally die.

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So you can live. So an observer, according to our current theories,

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understanding black holes can live for quite a long time inside a black hole and could make measurements.

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So it's interesting question to ask. What would such an observer see?

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And maybe we can discuss that later on in the question, not secessions.

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We can also consider a hypothetical Blackhall investment earth mass,

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and if you crush us into a black hole, it would have size just under one centimetre.

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So this gives you an idea of the sizes of some possible black holes actually physically realised and possible hypothetical ones.

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So what does the solution look like in equations? Well, we're talking about General Hibito.

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You have to talk about the spacetime distances. Nature, geometry.

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So here we have the S squared is a spacetime distance between events.

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And this is given by this expression involves four coordinates. Two of them are just the normal angular corners D, Theta, Theta and Phi.

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And this is just saying that everywhere there's a normal one. Spherical behaviour circle, symmetry, behaviour of the system where.

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That's the area of a given sphere is four pi R-squared.

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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,

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this denominator here is going to zero. So this factor here, there's an infinity that's appearing here at Times Square.

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And this is telling you you get radial length contraction as the Iraq horizon is approach.

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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.

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This is saying that according to a static external observer, right far away from the black hole,

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that as time dilation, as the horizon at a shorter radius of approach.

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Right. So so there's both time dilation and radial length contraction.

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Mr. Secretary. Well, that's in equations. And of course, you can study this.

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Great, Lena. I want to emphasise that the more longstanding of classical black holes is due to record a number of people.

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Wheeler, who coined the name Black Holes,

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which will see libraries as somewhat inappropriate name and thanks Kruskal occur Thone Hawking and especially our own Roger Penrose.

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And I think Roger made the greatest contributions to modern sounding of classical my calls.

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So what are these awe inspiring objects look like? Well, here they are.

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Here's a lovely little Etsy baby black hole. You can purchase for the low, low price of just 10 pounds.

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Here's a baby black hole accretion disc for astrophysical black holes have accretion discs.

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You can get these things with adoption certificates. That's lovely. Here is a different picture of what a black hole looks like.

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We can take this geometry. And of course, it's very hard for me to represent the geometry of this situation in two dimensions.

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But let me try. So this is a picture of radius and time.

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He? S each of these points you should think of as a particular four dimensional thing,

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as a as a two sphere sort of living about every one of these things.

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And what I want, I emphasise is as this is the exterior. This white region is the exterior geometry of the black hole.

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And then we have this horizon.

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And the crucial thing is as you go inside your eyes and in fact, Space-Time itself is not really static inside the horizon.

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The reason is, is because you don't get a hint of this from this thing as you go are is less than our.

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Notice that this term here changes sign. And this thing here changes sign.

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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.

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And that means this now becomes a spatial like coordinate. And this is the temporal called note here.

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So, in fact, there's a definite different a Kornet system where you see this having better.

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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.

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So, in fact, as you're going on with this thing, in fact, space time itself is dynamical here.

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And is dragging you towards the singularity as you go down.

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So as you see this picture being animated here. Well, as I emphasised before passing the horizon, nothing special happens to you.

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There's no infinite forces. You don't necessarily get ripped apart.

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The horizon of freely falling observer just thinks the horizon is very much like empty Minkowski space.

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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.

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But we should be wary about this because in fact, the classical solution.

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And in fact, Einstein's classical generals, hefty itself is not reliable here.

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So I want to emphasise to you that you that even though the singularity is predicted by classical general relativity,

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we know the theory is not really self-consistent here.

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So we believe that itself consistently describes exterior geometry and near the horizon.

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But once we start approaching the singularity, we don't know what that physics is.

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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.

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And so here we have radius again. So here is a star collapsing to form a black hole.

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And here we have an event horizon forming. And so the crucial thing about the event horizon is here.

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Here is drawn are light cones. So this.

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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.

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And material objects, massive objects always travel less than the speed of light.

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So I always have to travel with inside the light cone. So signals can only be sent in in these angles here.

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So this one here is ingoing light. Right. And would go into the.

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We go back into the black hole. But this one here would escape to infinity.

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But there's this distortion of space time in the black hole background.

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And what happens is the light cones tip over.

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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.

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All material objects inevitably go get dragged into the singularity.

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That's the only possibility. And ingoing light rays, of course, go very quickly.

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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,

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forward in time becomes radially inward.

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All right. So that's the thing.

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But there's another thing here, which is, again, a freely falling observer, a freely falling observer going through this system.

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I mean, we'll go through the rent rising, hit the singularity. But nothing special happens is really falling observer.

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She through force, through the horizon. It's just the usual finite tidal forces.

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You always get when you're in the external gravitational fields.

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All right. So there will be tidal forces on this person who is a tiny black hole.

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These tidal forces might be strong enough to rip the person apart, spike spaghetti for her.

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But otherwise, it's a large black hole like a galactic centre, black hole falling through horizon of such an object gain.

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Nothing special happens in the observable survive. A human would survive.

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And only when you finally get to the singularity, which should be destroyed.

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And so I emphasise, if we go back to the metric,

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it looked like there was apparently singular behaviour in this metric near our equals, our s, and that's why.

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And in fact, took roughly 45 years or so before people took black hole solutions seriously, they thought.

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In fact, this wasn't sensible. This only could be used as if it was a mathematical artefact.

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But later on, it was realised. In fact, there's nothing singular about this solution apart from right at the Singularity Arkos zero.

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In fact, this apparent singular behaviour, the short geometric, is just a natural supporters.

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It's like longitude. If you're at the north and south poles, it's a corner that breaks down.

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It's not truly physics breaks down at the event horizon. So that was that.

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Now. We now know to a very, very high degree of confidence that supermassive astroparticle black holes exist in galactic centres of most galaxies.

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And so here is a little movie, which I hope now plays.

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So this is pointing towards our galactic centre and it's starting over a whole bunch of years, the motion of the stars.

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And what you see here is a right at the galactic centre.

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This is a tiny distance, 10 light days that the stars are orbiting around a very massive, very centrally concentrated object.

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In fact, there was a Nobel prise shared with Roger Penrose this year in 2020,

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where these two teams, led by these two investigators, independently show.

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By measuring the trajectories of these seven stars. Right. Close to the likely centre.

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They're not they're not perfectly on ellipses.

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In fact, there are general relativistic effects exactly of the kind predicted by General 50 in the background of a black hole.

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The slight distorting these lipsett. So this is a confirmation.

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You have a supermassive black hole with a guy with a very high degree of confidence at our collective centre.

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So recently we have a direct image of a supermassive black hole, not in our galaxy fate in M80 seven.

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This is from the Event Horizon Telescope in 2019. And here is the shadow, the event horizon.

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And here is the accretion disk. So just like that little Etsy toy you can buy here.

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What the light is coming from the accretion disk is the black hole. And here is the shadow of the event horizon.

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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,

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but we also now here in the sense the sound of black holes merging through gravitational waves.

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So, again, I hope you can just click on this thing. Sometimes it's worth.

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Do you hear that sound, doesn't hear the sound? I hope so.

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It's so that is the sound. It was picked up in the gravitational wave detectors,

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the advanced liger collaboration that they have two sell at Hanford and Livingston in the United States.

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And this is the sound, the final chirp as the two black holes, two very supermassive black hole, actually, not supermassive.

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Very massive. Multiple solar masses are rotating together and finally colliding and they merge.

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And during that final seconds there,

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the energy released in gravitational waves far exceeds the energy produced by all the suns in all the galaxies in the universe.

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It's an extraordinary three or four solar masses worth of mass are being converted to energy, almost alling and gravitational waves.

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And so now we've seen dozens, actually hundreds of black hole mergers.

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And so this is merger tree of how black holes of urging, merging and evolving.

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And of course, it's nice. Let's see thing.

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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.

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The final black hole produces a highly spinning black hole. So it's not a short, tall black hole, but the astroparticle black holes.

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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.

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Okay. So the summary is, is we know there's a wide variety of black holes exist in our universe.

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And they're very well described by Einstein's by this virtual solution or the curse solution.

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It's generalised the rotating generalisation in external region.

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So my interest, though, is quantum black holes.

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That's what I want to tell you about. So the classical theory of black holes is extraordinarily rich.

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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.

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And what we are going to find is even more remarkable in the classical case.

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And it apparently leads to deep paradoxes and these deep, dark paradoxes, rather like the birth of the early history of quantum mechanics itself.

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The thinking about these paradoxes and understanding how they're resolved is

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guiding us towards a much better understanding of aspects of quantum gravity.

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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.

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All right. Next slide. So the first thing to realise is the most basic quantum facts about a black hole is hawking radiation.

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So let me tell you about why what hawking radiation is and why it exists.

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So in relativistic quantum mechanics, sometimes we call quantum field theory empty space, quote unquote.

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The vacuum is full of quantum fluctuations of all fields and particles.

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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.

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This is on a five Fermi cubed lattice.

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And this is a a time loop of it. And here we just have one realisation show we spoke to Super posed a different

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quantum superposition and we have different positions of what the vacuum is doing.

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This is one realisation. And you see this thing is fluctuating like crazy.

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We're getting fluctuations of scales that you see.

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There's a typical sort of scale here that set by the scale of QCT, its self, which is Voda itself about one Fermi.

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Right. Or 200. I mean, the Lambda QCT. So.

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And instantly this is verified, these cutey deep precision calculations.

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And now give you quite accurate description of the low lying masons and baritones and various other states, other properties.

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We know this is true. We know quantum motivations are there for many reasons. This is one demonstration.

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So what about hawking radiation? Well, so here we have space time and here's a black hole.

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And as I emphasised, at least near the horizon, it's just like empty Minkowski space.

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So we have these positive and negative energy, virtual particle fluctuations happening everywhere.

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We have them happening outside the black hole. We have them happening certainly in the region anterior to the black hole.

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As long as we're not very close to the singularity, we don't know what's going on.

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Singularity, but certainly in the region around the horizon, we have these virtual particle fluctuations.

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I won't ever size the particles antiparticles here, but is the crucial thing is whether they're positive or negative energy overall.

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These things have zero energy. All right. And there is a correlation between their energies such.

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They start off in the vacuum, go back to the vacuum, constantly doing this.

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Well, if you have one of these fluctuations in the vicinity of the rise in the black hole,

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there's a quantum mechanical tunnelling process that allows the positive energy guy here in red, which could be a particle or an antiparticle.

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So I don't know, you'd get confused. It's not always that particles come out of the black and antiparticles go in.

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It can be either particles or antiparticles can escape. The crucial thing is whether they're positive energy or not.

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So rarely is tunnelling process allows a positive energy particle or antiparticle to a state to infinity while its negative energy sibling.

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And this is negative energy from the perspective of some distant observer particle or antiparticle is captured by the black hole.

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And therefore, because it's negative, energy reduces the black hole mass. So the end effect of this is the black hole.

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Mass has gone down slightly and its energy has been radiated away to infinity a little bit.

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And I like to experts here, this is sort of sometimes given as an intuitive picture of hawking radiation,

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that this tunnelling picture of organisation can be made precise.

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And he has an interesting advantage over Hawking's original calculation that actually explicitly shows the black hole mass is reducing.

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In fact, in Hawking's calculation on deficit of it maybe is that it's on a static background where the

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black hole mass is not reducing these tunnelling way of thinking about hawking radiation. In fact,

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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.

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So the end result of this is physical black holes are never truly black.

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In fact, they produce thermal radiation, all climatically allowed modes.

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And here is a little cartoon. So I went inside dominantly for black holes. It would be gravitons, photons or maybe neutrinos.

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But in fact, in fact, all kinematics available modes are allowed. So amazing.

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End result is black.

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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.

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It's a quantum effect. C cubed over eight pi. Newton's constant.

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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.

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Imagine we had a kg sized black hole. That's a logically consistent thing to consider though.

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Hypothetical, and since we've never observed such a thing, it would actually have a very high temperature.

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Ten to twenty three, Kelvin. So it's not like this is a small temperature, at least if we have a small black hole.

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This is a very large temperature for a small black hole.

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On the other hand, because astrophysical black holes are so massive, solar mass for solar mass.

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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.

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The Hawking temperature satellite.

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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.

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Well, it would start radiating energy. It was mass will work with we all juice and therefore its temperature will rise.

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And there's a runaway process here. So that's important to bear in mind.

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I want you to remember that for Lytro. So Blackhall Hawking radiation has never been observed.

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But we have a high degree of confidence. That's true. We now know many ways it could be theoretically derived.

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And it solves some otherwise troubling aspects of classical black hole physics.

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Let me tell you a little bit by one of these quite troubling aspects.

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So one of these is associated with a second law of thermodynamics, which, of course, is that the change in entropy,

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in a physical process should be greater than zero or equal reserve if it's reversible.

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So Fleckenstein argued that to say the second law one must sign and I want to emphasise is a finite end to black holes.

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Otherwise, one could systematically reduce the entropy of the universe by throwing in matter with entropy greater than zero, which then disappears.

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All right. And if you do not assign any entropy to the black hole, then you reduce systematically the entropy of the universe.

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By doing this process, by just quantity recycling this process, you could use it with universe.

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This is a pretty bad thing. So Berenstein suggested, in fact, that the entropy of a black hole is fine.

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Entropy should be proportional to the area.

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The black hole and Hawking's calculation of the temperature confirm this because the first laws were seven.

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Amik says d e equals temperature times D.

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S with the E is the change in the energy. The S is the change in the entropy.

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And we now have a formula for the temperature due to Hawking and we know the energy.

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Here is the massive black hole time C squared. And if you put this N, you put the formula in for your tea.

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Hawking arrived earlier and you put in what you just take the derivative.

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This thing, d.A. So it's just the M C squared. You can then find what the change of D.

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S is D. S and integrate that up. And what you find is you find this expression for the entropy of a black hole.

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It goes. This is called the either the black hole entropy or the Berenstein Hawking entropy.

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It goes like CS cubed on G Newton one over H bar.

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And then the area, the black hole on four.

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In fact, this combination of units here, this defines the planked length squared or the one over the Planck link squared.

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Another better way of writing this is one quarter of IE.

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The area of the black hole event horizon over the Planck Link Square.

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I want out I want you to notice this Planck length squared is Planck length is incredibly tiny,

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is approximately ten to the minus 33 centimetres and black.

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Oh, of course. Black hole of enterprises. Well, that macroscopic things there.

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You know, kilometres squared or much bigger banks.

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All right. Or much bigger for supermassive black holes.

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Now, I want to emphasise to you that here. Notice isn't one over H bar here.

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So that means the classical limit. Each bar goes to zero. The entropy of a black hole in the classical limit will be infinite.

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And this is why you can constantly keep highlighting entropy there in this process. Why should you?

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Homer Simpson falling into a black hole. So this should remind you of the catastrophe of plis pre plank classical black body radiation spectrum.

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The fact that the quantum effects actually make finite insensible what will be an infinity in the classical theory.

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That's very interesting. So that's one way of thinking about this.

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Well, one way of thinking about the meaning of this entropic formula that the entropy goes like one quarter.

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The area over Delplanque squared is as one cubitt sorry, one cubic per for Planck areas for the arisan.

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So here is the event rising, divided up in little things.

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And there's a cubit, you know, either zero one basically on average, one for every two or four triangles or Planck areas here.

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So this is a very, very rich and complicated system, has an enormous number of cubits.

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Let me tell you about that. Well, the entropy if you put in this formula for a solar mass black hole,

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you find the entropy is a vote would attend to the 77 times the mass of the black hole over M Solar Square.

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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.

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In fact, because these guys like mass squared and we know there exist supermassive black holes,

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the entropy of a super a single supermassive black hole exceeds the entropy of everything else in the universe.

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So that's an extraordinary statement.

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Another way of thinking about this very large entropy is quantum black holes of thermal systems with a huge number of microstates member.

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If we take member Boltzmann's famous Formula S is.

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Well, let's forget in place of constant Essy was log W with W's number of microstates.

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The system, which says high then exponentially therefore misses a number of states,

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is approximately exponential of this century and this century is already huge.

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So the number of states of a black hole, a low lying state, so black hole is incredibly large.

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It's bigger than Google, vastly bigger than a Google.

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So this has some comments. Well, the information content of the universe appears to be hugely dominated by black holes.

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That's a remarkable statement. We don't understand well, these microstates of black holes, exactly what these microstates are.

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There's some progress in string theory, but aren't sending is certainly not complete.

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Very interesting. Late this Entropia respected site hawking entropy or the black hole.

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Entropy is not extensive. It goes with area, not volume.

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It doesn't go with mass either. Goes like mass squared because it area.

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This leads the idea of the holographic principle which motivates mouther signer's actually

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very specific and concrete thing called A.D.s CFT duality for certain space times.

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So this holographic principle says basically that the infinite information content of a region goes like the area,

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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.

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This is an incredibly rich area that deserves an entire morning in itself.

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I don't have a size that we understand holography reasonably well, inequitably curved space time.

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We don't understand Flatt's white space a lot graphy currently.

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So that's already something remark. We got out of black holes. But let me turn to some other implications for creation.

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Well, since hawking temperature increases and decreases black holes and explosively evaporate

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by runaway hawking radiation and the end temperature of hawking evaporation,

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a black hole is almost planking is incredibly high temperature.

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So this means that hawking reparation is quite extraordinary.

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Every particle in nature with mass less than implant overwrite pi.

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So that's about 10 to the 18 G.V. can be produced even if it's completely decoupled from the standard model.

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And the reason is nothing. Hisam gravity. This is not using evaporation.

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Occupation doesn't depend upon a particle being charged or colour charge or anything like that.

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Having company Salmo nothing hisam gravity.

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Therefore Hawking evaporation is a scan over all of creation, even things that are hidden from the standard model.

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So this way you can produce, for instance, dark matter or even start a hot phase of the big bang.

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And so I've been investigating these issues with my students.

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These are three of my very good graduate students here at Oxford and Olivier Rudan and Hannah.

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Two of them, I think, are in some of the breakout sessions. We have to talk, too.

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So this leads to what could be observable signatures and hawking radiation, hiding in dark matter and in gravitational waves.

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Adam, very sadly and of course, whole Steven himself.

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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.

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So this is quite incredible. Why was Ms. I'm surprised. Yes, there's this possible observable signatures hawking radiation, but there's more.

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Right. Adam, coking evaporation applies a remarkable consequence that many for the theory, including gravity,

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there are non spies and non spacetime global symmetries or with violated this approximate at best.

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So let me just quickly describe this mean what this means.

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This means you can't have exactly to generate physically distinct states without him such internal symmetries.

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You can't have an exact quote. Zack Clay. Every potential surface.

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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.

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So if you if you slightly violate this symmetry, that means the global charges are not conserved.

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So one example of this would be the non conservation of barrier number, for instance,

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snapping not normal Yousafzai Baren number with some you won global symmetry with this must be violated.

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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.

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So you crush these neutrons to form a black hole,

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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.

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It only cares about the mass spin in charge of these states, not whether they're baren anti barium.

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So at most the final state has plus or minus root end of of Barry on charge here.

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The blue there's one, the three blue and one reds is one net state.

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Here we started out with a lot. So you lose Barry a number in this process.

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So global symmetries are violated by hawking evaporation.

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Now, there's a we don't extend exactly how this works.

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And for generations in particular, we don't sign a form and summarise the global symmetry value interactions.

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But there's progress, again, by by groups involving me,

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but other people as well around the world and progress, recent progress being made on this issue.

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That's interesting. So I'm almost done. Let me make a few final words.

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So one issue I haven't spoken about is if quantum mechanics and black holes are, in fact inconsistent with each other.

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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.

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Roger Penrose is you. So what is the reason for this?

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Well, hawking evaporation of black holes appears to allow for quantum mechanical, pure states to evolve to mixed states.

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If so, this would be of would violate a fundamental axiom of quantum mechanics and imply information loss.

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But in the last two years, there's been major progress on this issue and a consistent calculational framework is now emerging.

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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.

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And what is their basic idea? Notice that some very exciting things here, replica wormholes in the black hole interior.

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This is trying to understand in a real way what is the physics of the interior?

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What observers who fall through the arisan would sees is crucial in understanding these issues.

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And you're having some very interesting things like wormholes appear, other kinds of solutions possibly to Einstein's equations.

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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.

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In fact, we always knew that it had his calculation had loop effects there.

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But in fact, the paradox was, is all these local quantum field theory loop corrections don't help solve the paradox.

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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.

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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.

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They're incredibly tiny.

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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?

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And the answer is, if you compute the radiation, the entropy of the radiation is coming out.

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So some other states of the eigenvalues of this density matrix and these eigenvalues

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now shifted by exponentially small amounts because of these tiny corrections.

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But there's an exponentially large number of states here.

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Remember, emphasised before that the black hole was an he let excellent large number of states.

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So there's exponentially larger number of terms times, exponentially small corrections to each one of these terms.

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And this can lead to an order, one modification. And in fact, there are demonstrations in simple cases that this purifies the final radiation.

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So leads to pure state to pure state evolution, meaning that quantum mechanics is consistent with black holes.

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So I want to finish there with a statement, the quantum mechanics, black holes is even more remarkable than you might have thought.

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He's guiding us towards a better understanding of quantum gravity, and I emphasise information as well.

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And so I think is very good reason to believe that black holes are quantum black holes.

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And think about the hypernatremia 21st century. So I'll stop there.

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Thank you.