They did not think it over. So the legal discussion about polls in 1970 and beyond the outlying peaceful
and personal reminders of intensity and vigilante response time by people,
opinions and rhetoric. We'll talk about quantifying this relationship.
And that brings us suppose.
Then we'll discuss the most fundamental solutions of general relativity, such as washing, first, personal notes, the tests on human efforts.
And then we'll come to political discussion of that crisis discussed in this article versus course, the literature.
Before coming to the more advanced topic that involves loss of mental mechanics, then lost in terms of the likes of the real system hawking radiation.
But whole entropy then will come more smoothly to focus such as holographic principle, which you.
So first of all, we all go to some extent some people from high school, some people from popular movies,
or else we all know the problems of general relativity, momentum and energy curve spacetime.
They distort the science. And because of this distortion motion of other questions.
So exoplanets, libraries around the object that first spacetime change,
I mean different basically if you have like great synergy and so large quantities of space time,
the delay train will look up to get slightly more it will be disrupted by the for
simply the fact that the drug is still in the property will throw things curves.
So this is the quality to future discussion is over. Quantify this and quantify this.
We need like old equations before the question to fulfil general relativity or even above 100 years ago.
And they are Einstein's equations written here and discussing some to behold.
So basically the context of general relativity is the geometry, which is metric will be affected by energy for mass and vice versa.
So what are the ingredients of Einstein's equations of motion?
The main hero of his discussion? The beauty of the magic.
So let me remind you the simplest facts, such as in front of us,
we have a two dimensional flat space and it will take the measure difference between points B and C,
for example, distance built S, then the distance is given by the firm to see the distance of a square you simply equal to the x squared plus no force.
Then we can take the distances to be small, and then the same line, but no difference.
And it doesn't. The small elements applies. We have here squared is a small element is equal to x squared plus twice square.
This is the metric of two dimensional space time.
We can generalise this for three dimensions. Here squared is equal to the squared white squared plus none of work is that squared.
If in fact, Weisskopf is contentious with the headlines in the last four or five six dimensions if necessary.
And so you get dimensional, you get dimensional flat Euclidean spacetime.
The light element squared is equal to the sample squares.
Obviously he doesn't want these displacement.
We can put this in the more elegant form metric square by right controlling the threshold need a squared is equal to g i g.
He explained the energy where summation over energy is assumed.
So this example is given equal dimensions.
So I'm saying go from one end to issue because one and two, and in the end you should get 53 just like the x squared plus the iceberg.
So explicitly this relationship is given here in this line we have four elements already.
We saw over 83 that are for energy,
one long if you include you want energy pool and these four elements you'll be unable to put into numerical metrics such as you here.
And we can compare this line to this line and we see that these two of the elements are
equal to zero and g one is a good one and should have at least in this one as well.
So this is a metric comes up in fifth dimensional space, so most of which is like this.
So in the previous example, G was independent of absolute just in metric cost of metric six one and 100,
but in principle it means about four points in space for this time.
So for example, we didn't have to name the three dimensional space, the square in which three can use a square.
But another one important thing. But we can use different coordinates.
We can use for the same three dimensional space. We can use either official coordinates or circles.
Origins are shown in this picture, and then the left element will change physically from this.
Look, it's just not surprising because if we change versions of the discussion with this, the squared will not change.
But of course these orbits change and therefore the metric itself does a must change.
So in this form it means that in the first case, which is 3.33, we with the last one on the yellow in the second case receive a symmetric no.
Depends on the point in space why the exclusive dependence on space?
It will be important to discuss equals.
So some examples of the metrics here.
So this is a metric in the field of admissions.
Now we can generalise this more, and this is the performance of a social media, which is scholarly, getting made by inside and others.
That's the reaction at least, at least locally in four dimensional spacetime where this is a spatial can't get a squared away.
Squared is indeed so squared. But the thing is not an independent spectrum.
They need to put also the time elements into the metric.
And essentially the cosmos of special relativity is that our spacetime is locally in cost, is beside the dimension given here.
Again, you can write this metric avoidance, for example, in circle coordinates.
And again, the same 11 point is two squared squared.
But this part is written in certain importance. How do we know that our space spacetime is actually current?
What kind of local experiments and vocalisations can we do to determine the curvature?
Oh, so it's like this. Well, some people talk about this whole time.
In particular it goes and then it's actually one of the local experiments is the law is
that you can draw triangles and try to measure to solve the angles in the triangle.
You just based on the set, you discover that to some of the angles is equal to 100 degrees.
If it is not, for example, which handles here,
you can measure bicycles and discover that the sun exceeds all other places if your space happens to be the cell is one thing,
this one, but just the charge and then the triangle, the sum of the angles of 300 degrees.
So this is a test. One of them, you can do this, for example, do the same central point figure, which is on the public space,
the but just the space you can do the whole only you can draw a circle and measurements of
difference and you discover that in the secondary space discovery is greater than to pay.
Ah, this is where were in the prestige, which is also price a little bit to measure light elements in fact.
But what he sees is even less discretion with Weisler downstairs.
So this is all to Mexico City.
But then you only ask one. So how do you know for sure if somebody gives me this lecture?
Is it surely the fact that the space is curved or you can do some important information like in the previous slide from circle for just
to partition apartments and actually being the centre for some complicated information back to the flat space is impossible enough.
So we need to have some local test of possible lots of space is correct and such a local test is provided by three mountains.
So what will believe that? Explain what this object is. It's the dirty dom so you can only know it is two fold.
In fact, it's not very well done. So the thing are derivative of some object which is known as the free stuff and connection is not the simple dharma.
And this is such a simple domain itself. Depends on the metric.
So ultimately remote answer is inexpressible in terms of derivatives.
Actually the second image, because it's one third of the way here and then on top of that there is another derivative for God.
So it is a second value, which is called the metric,
which reminds us of all the human desire you can build other important ingredients such as nature comes up and reach stellar.
And the important local statement is that the space is slept even only if its human presence is identical as you.
So you somebody goes to and tries to sell a very complicated poetic statement.
I found a wonderful solution of Einstein's equation. The space is curved and this is a solution which would be named after me.
So you should not. Belief is first, if once. First of all, you should check that the optimal design of this metric is you by holding these formulas.
And if you discover that the human does zero, then that is the existence mission which brings this complicated entity back into the vertical space.
And therefore the claim just in this so the even and it's the images will play a very important role in general energy.
Of course as we saw already you as on the basis of the piece begins in alcohol.
And here's what I don't think we should send you to the equations.
You already are. So let us have you. On the left hand side is basically the second order partial differential equations for the metric.
On the right hand side, there is an object which is known as the stress energy density.
This encodes energy and matter contained in space.
So important statement is the following.
Despite the fact that you don't see any of the images explicitly entering here,
the equations the oh is this all the previous like the are second order nonlinear coupled
partial differential equations for the components of achieving you which by the Mexicans.
Okay, so you can I tries to magically carry the expression of what you're saying is equations of the left hand side.
So you could see that indeed. The second order of operations and the source of these equations.
On the right hand side, you can compare it his muscles equations where he has a point to support the distribution of charges and currents in space,
and he would like to find electrical magnetic field generated by those studies.
Then write the muscle equations. And these are also partial differential equations with respect to the for potential a new from Amy.
We can cultivate EMV electrical within the field in more space.
So the velocity is the same. The electrical magnetic fields here are sourced by distribution of charges of cards.
Here the method to renew is source by distribution of matter and energy in space.
There is no fundamental difference in these equations.
Lots of situations are linear. This means that we can find the generic solution, if not explicitly done in the form of some integrals immediately.
And people in 19th century did exactly that. However, here I'm saying equations are possible.
Moving their differential equations. Generic solution is not known.
It is not unique. It is very, very complicated.
Set of differential equations. So you are in a similar piece because you decide you will consider zero metric sources supposedly.
Tell us what you. We don't have any sources that I can cite generic solutions to non and you're going to call them yes.
Situations for theories, which is also a very complicated set of equations and solutions.
Will you? However, solutions into highly symmetric species can be solved by making assumptions about ultimately, for example,
if the source is surplus emission, we can assume that the solution will be strictly symmetric as well.
If the source of the left hand side will be strictly symmetric, such as the distribution of mass and uniform distribution of press and surplus.
Maybe we can make an assumption about the light elements.
We can think that it will be certainly symmetric.
That means that the ends A and B here will depend only on the radial distance from the centre,
but they will not depend on the angles because it is a surplus energy and this is a possible assumption.
So look at the next to substitute the solution. This answers to the equations, emotion and so forth a and B with appropriate public positions.
And you discover so that Moscow Schwarzschild did in 1916.
You just tell and we'll just all just dishwashers. But one of the most important solutions of journalism.
So be sure to read this you'll hear it describes this magical spacetime outside of the point of mass, just outside is extremely important.
So if you look at the message, it's not so different, different from this.
I mean, of course, you are breaking similar to this little element here. You jam over a C squared.
Ha, it does a circle here. If you've got just a zero this vessel, then you're back to the boss dimension.
This element is actually just these is actually not very large.
So corrections to this one is very small.
Four stars is limits. So you can think I mean, if you think of Earth as a start to symmetric body, then even estimate what this action is.
How much is based on your skirt? All right, here. I'm sending you, don't you?
Because what you are and you calculate the selection, what actually will be on the order of total minus nine.
So it's a rather small distortions based on colour and it's still sufficiently large to affect, for example, justification specifications.
What the thought of this very simple. Derek So this is about the logical it seems at a certain point, but this whole bracket becomes you.
What happens? It's a so-called short term reduced and part is equal.
Each question squared. Then this becomes you and this becomes you as well.
Therefore this term pulls up. Well, something happens specific and we need to investigate.
Look, exactly. Well, remember that the graphic describes this based on outside of the body of Miss M so for most object this pathology this is clarity
is not is of no consequence is of significance the most object the shortest Regulus is located deep inside the object itself,
and therefore is not an element of a solution because the solution is on the very top side, but it's from the earth.
You Schwarzenberg This is about one centimetre, so this is the whole issue and a solution is so of this is, this is, this is the earth.
The shore surface from the British is somewhere deep inside and the solution is hold it outside.
So you don't, you don't worry about the house inside. There is a different solution that they want you to write inside.
Inside this inside the solution of the sun, the shortest radius is kilometres.
And again, this is a tiny, tiny distance deep inside the song.
You don't worry about the solution there because the solution is very complex.
However, something comes if some violent forces will squeeze all the matter of the star or split in two inside dishwasher days in the case of.
We'll get some political indications from the logic yourself.
So you remember this piece Inside Dishwasher videos, for example, in the process of the rotation of Pop Superstar.
Then we got the bullet hole and this is where our problems start.
So then we have to take the spectacle of this kid celebrities very seriously.
First of all, you have this well, there's all this events item that are equal to our forces.
Then this thing becomes zero. And then there's another singularity in the metric, not just scared of you are close to zero.
Then this whole term goes up and the same happens here. So there's another singularity in the metric that are equal to zero.
Well, we need to remember that the metric is actually, in terms of issues differently in different partner systems.
You change the importance of words. And you can think of something here.
For example, in two dimensions you have the addition words, light elements.
Let's face the x squared plus y squared. You can write the same line element in polar ordnance and you can see all bets are equal.
Zero. We have a pathology similar to what happens for schedules.
Right? This whole term does appear historical.
So but we know that going can make it more automation back to the properties of space and points of origin.
Zero is no different from any other point in space.
So this is a board, this is military, this is this is a single entity that we can get rid of by changing the change in performance.
So in a similar way,
we'll get breakfast Russian Federation different board does a couple of things is violence and the vegetable is equal to our s law.
Population of Baltimore boiling up a little curve.
However, something will happen as we discuss in the next slide in general to check the story coordinate similarity,
we need to compute something to see some variation coordinates a change because we need
something that does not change for the change in system or just a couple of competitions.
The polar analysers and special variants.
One of them is called differential variant. It is it is basically a product of three methods of reporting.
This is support for a first metric.
This special variance is a version of the one or 2 to 6.
So this is completely normal people. There are people who are pushing these similar laws up as far as possible.
So after that, this encourages what we want is a truly nonpartisan letter, an article to see what we don't know.
We need to modify physics in order to understand what these articles yield.
But we don't need the money. If I just focus on the central problems that are economical solutions.
So what happens at such a high speed?
Something isn't covered. Sadly, the president began to study emotional particles.
Light rays got all black holes, just like to study the orbits around the star or or any other source.
So let's think about what comes to light. So curious what happens to special abilities, right?
The special relativity. If the observer is looking at this here, it's going to be right somewhere in the centre.
Then of course it must light forth. And the future light cone, which means yes to particle for example, a massive particle does not propagate,
does not mean in the natural cycle this observer just stays there.
Then it simply propagates along with that next plane goes up.
If this particle has some velocity, no matter how small, it will not stay on the same space point.
It will move in space and therefore it will move on this graph,
the sum endless flow and the slope will be equal to the speed of the motion of this particle.
So the maximal speed, the consensus, will be the speed of light.
And this response to this, they are going to they are going to motion along the surface of the light pole.
So problems like trains will move in the future along the surface of this well, this small and therefore usually.
So let's see what happens to problems in the vicinity of the black hole in the centre ties.
So here are these light poles drawn locally like poles outside of the prison.
They look more or less like in the special relativity.
But then you come closer to the horizon with ideas of these, become a little bit squeezed and a little bit delivered.
This is a property, the virtue of spacetime.
And then so you can follow these, this, this and a little bit like and the light from this point, for example,
will only propagate inside the light forms and let them only propagate inside this little,
little region here which emanates from this from this point.
But now it's coming through the glass horizon.
You can see the table, the fish use light bulb to comfort the garden.
See, our axis becomes what you find. It is a third for all photons which which emanates from really begin to look like from here.
In here they will only propagate inside this region which is bounded by the event horizon little.
Never come outside. They can only come inside the inside the size of and eventually they will end up and are
equal to zero 30 similarities and where we don't know what kind of physics this had.
So this is the property of the event horizon which is compatible with our understanding of the black hole in sort of the normal terms.
Right. That separates the body is very strong. There's nothing even like the whole scheme just doesn't work.
So let's see what happens in terms of the more advanced physics and the limits of quantum physics.
But of course, so again, this is a question magic. And you may ask why?
So what do we go? Well, this is very genius. The answer is, unfortunately, after a hundred years of Jha, not so much.
We know a great deal about the behaviour of particles in fields around horizon, but we don't really know that it's happening inside some literature.
One thing to remember is that general relativity is an approximate field.
It's not the last word, it is. So here's an example of a branch of general relativity where Einstein's equations go from these two terms,
but you can easily write down all the terms which are ends and therefore they can handle the action.
And at one level they must enter the action according to the quantum democracy.
And if you observe these these until you discover connections between science equations,
we don't know at the moment what kind of conditions enter these directions.
But generically we can see but you can actually see are expected.
So sure. But it does not give us more than a little bit corrections to the message coming from the
so-called Holy Week first and also coming from quantum quantum groups like Constellations.
Again, we don't know the future with it at the moment. You can think of unity as the fact effective theory if large distances some time.
Compare this again to students.
Yes, situation describes the motion of essentially any truth, but we know that for a very short distance the fluid is discrete.
We have molecules, you other pseudo and so on. So it has a very complicated structure which is not captured by not just those equations.
In fact, you can generalise them.
Just those equations become closer and closer to this, to this distribution of these molecules and discrete just of fluid.
So similarly, gravity, if you want, you can think of energy as a simple equation equations.
And some of the equations which describe this fluid is sort of looking through the spacetime without looking at the fine details at a very,
very short distance. We don't know what it is. This is the frontline of the modern particle physics.
So let's briefly discuss all the solutions of intense equations.
One of them is relational, not observation. This is a surplus distribution of mass ethanol.
No charge. Q So look at the metric. It is all the Schwarzschild metric.
This is an example of this traditional term here, which depends on the charge.
So now all this ball is, is, is my system is also has an integral charge.
Q And so we have this term here and this term here.
It's a good chance to go back to first metric. If not, then it is a generalisation.
The not just something has to be closely held while the r squared square equation
will give us the Horizons presence inside the solutions for the extreme solution.
And it's very important to think theory of issues.
All right, then another solution is even more important. It will solve by Roy Care in 1963, not so long time ago.
It is a solution which discussed danger, excellent symmetrical charge, distribution of mass.
Its parameters are mass angular momentum. J So there's is a complicated metric also that comprises and the reason for that is you're in between them.
I'm not going to tell the kind of metric, just notice that is not a solution.
So you can say while taking charge that the solution will solve.
So you're going to have to take an absolute symmetric charge.
Distribution of mass, but only does not completely dislodge just the whole loop in mass charge from the governmental j.
Now let's go to more advanced topics.
The portable Civil War games started by Jemmy Carter in 1973, after studying the metrics such as questions, graphics, cards and quantitative graphics.
But he does support the decision of law that says the horizons of a station in the pool.
It's also surface take. You can see the surface reality as the analogue concentration of people.
G nine point basically 4 seconds square. But no, no. Here, look at the eyes of the black flesh.
That's the kinds of issues important for description of the police.
The first law tells us, but the valuation sufficient must post the change at best is related to the change of charge.
At the moment, the change in size is area by default in quantity equation.
So if you if you look at five of the whole symbol, you think it's to the whole increase the mass and all of a sudden it just will increase.
However, the second law tells us that the crisis area is a long, decreasing function of the volume of the piece and the third law.
It is impossible to achieve zero circles, very focussed costs.
So what you can do is to compare these four laws of level against the laws of thermodynamics,
and you find the remarkable, remarkable coincidence if you want.
Or maybe it's not the constant. So the zero 400 X tells us that the system to solve the problem has a constant
temperature gene that is very similar to the zero four but negates the first of all,
from the nexus of all conservation terminology. It tells us that if you change the energy of that whole, the entropy of the system changes.
And the Russian work serves on the second law, which is an important work that tells us that the entropy officer of the system does not used style.
And the third law says that it's impossible to achieve too much. But if this whole process is just a coincidence, well,
if you just there's a deeper connection between the laws of platform against the laws of thermodynamics.
You are tempted, perhaps, to identify a couple to some conditions of departure and area and areas of the entropy of some of some system.
But it's not clear how in 1972,
just a big baseline suggested that the black holes should count as well defined entropy proportional to the horizon area as in the previous slide,
and was actually lost in very many of the searches because black holes are left with lots
and lots of information and therefore can also have a temperature associated with them.
So lot of it is false.
However, in 1974, Hawking demonstrated that the black holes actually borders on the Asian quantum level and so one in fact associated temperature cut.
So that was a rather dramatic advance. So here are some formulas.
So Hawking showed basically black holes can get radiation, a play for you.
Spectrum of the temperature given by this expression not is the presence of the H bar.
So it is a process which happens at the normal level.
And you can see from this formula that the Hawking temperature is inversely proportional to the mass of the black hole.
So if you have a supermassive black hole, its temperature conduction will be very small.
You can look at these numbers and hopefully for some, however, it's in black holes that are extremely small with all primordial black holes.
But the temperature will be sufficiently sluggish. So, for example, black hole of one solar masses of hawking.
So much of the ball is. So this fixes the additional analogy between science conjecture and the baking soda
entropy estimate is indeed proportional to the kinds of areas in Horizon area,
and I didn't notice the presence of each far downstairs.
So that's the immediate consequences and immediate problems which are related to this piece.
First of all, that whole elaborate the stuff you see from this expression, it's almost obvious that they have negative specific heat.
Right? So what happens if this is temperature? The black cold is suppose it's released.
Some of its mass masses decreases masterpieces.
This end becomes smaller than for a temperature becomes large, right?
And eventually this black hole will evaporate. The question is what comes after it lies in its liquid.
The spectrum is completely features. There are no imprints of any information which was ever thrown into a black hole.
So you can throw you black holes and you start to complicated systems, which some books.
So although some political systems contain some some obscure information and in the end,
the windfall of all the irrigation future distribution remains, it seems maybe we don't understand something in the very end of this process.
But it seems to me this is not just information lost, folks, which has been developed until until until now.
In fact, it's not going to clear, you know, what is happening then. But that doesn't mean I don't at all.
The most important question, however, is often what form the microscopic degrees of freedom underlined by most governments?
Remember, the thermodynamics is also, in effect, your theory. But in the usual systems we have normally microscopic level.
We go to statistical mechanics, this notion of temperature, entropy and so on, emerging from the dynamics of the microscopic quantum systems.
So the example of this, the simple example of this is the system of particles, the spin.
So suppose we have we have one particle. The spin has to make a state system can be up with up a few particles as a form of particles.
Then there are more options, Wolf. You just come down for a spin up for four the in the opposite direction so
that all together in one particle we have to like a states for two particles,
you know, for microstates.
Generically, if you have any particles to spin, the number of microstates is equal to the power and and also borders that the entropy,
the usual thermodynamic entropy on this preferential level can be completed as the location of the number of microstates and in this case the entropy.
You can easily calculate just proportional to the number of degrees of freedom of this composite.
What happens? A black hole with all the black holes, entropy, because I'm hoping to calculate the percentages.
But this entropy looks nothing like the states which we want to count in a similar fashion.
Maybe to get to get the centre to be in the lack of force can be called to make up this black hole.
And the problem that we can start talking is what are the microstates?
This is a fundamental question and people are tend to go for many years to solve this problem and there is a partial progress in this direction.
In particular, the strongest one probably is by strange involving 1996,
we're able to count the microstates of a very special supersymmetric black hole in five dimensions.
Yeah, it's a far cry from misfortune. Black call since in the middle of our galaxy ensemble.
But nonetheless it is. It is a model which achieves this success.
But the result translates exactly the defects that took it from.
The reason why they had to resort to the special repulsive magic level is the following.
What they do basically is it is a construction of things and the orginal object, the feeling, all the things you can count it to be complete.
You can go to microscopic states of the system, just like in statistical mechanics system of spin.
Then you squeeze this whole thing beyond this short radius, it becomes a whole and you can get the a sense, I mean,
entropy is easy to do and then you compare this to results, but you must be sure that in the process of reasoning you don't lose Einstein's.
So this is affected by supersymmetry and this other special problems, the bulk of special properties.
You cannot be sure you hope this is not the case, but they are not serious exactly.
But this is a major difficulty here. So strong and powerful results is the general life in many ways to find the right physics.
However, you still do not know how to find the manifestation of the normal level.
For example, the symbols that hold important dimensions moving less.
It does profound consequences of relations. Well, let's talk about this.
What about the principles for the learning systems and identity? The other is extensive proportion to what you think of the gas or some fluid,
and the entirety of the system will be proportional to the what is this gas such question.
But notice that because I'm talking entropy,
which we just discussed is proportional to the area because I is an area called not volume control system before you just proportional to the area.
And it seems that the gravitational degrees of freedom in dimensions generically
are effectively described by some theory you might have some dimensions.
This is known as the chemical principle, which was first discussed by Fulton Susskind in 1992.
So again, very clear. This is a great occupied in some way.
The effective degrees of freedom seems to be of the boundary of this of this region and move over initially.
So this development resulted in what is known as the eastern gravity,
sometimes also is known as few correspondence and is basically the same statement.
And he grew up. It's important to understand the Eastern principle as kind of those who are open of them.
This. On the calendar.
So in the open sea creature you have the of grains of low energy and it is the highest described by quantum computing development.
Some of you or someone, you squeezed this whole thing beyond the coastal radius and now you've got a closing feature that makes the strings.
Grains of low energy is described by very thin molecules in higher dimensions.
And you conjecture, the ideas people have on this is that the conjunction is by the fact that it survives many, many, many discs of it is just proven.
The conjecture is that this site is exactly equivalent to decide to do it in a session forward.
Like, well, the sentiment goes by looks profitable and we don't imagine that the solve.
So that's all good. So we know that's what I saw.
But it's a microscopic system that describes all black holes.
It describes some internal equilibrium because we saw what was a black hole for many stores,
and therefore these are identified as being cytokines, entropy and temperature.
But what about black holes beyond the people so uncertain because they're characterised completely by global charges such as mass,
both electric charge and those forms of momentum.
And so licensing, if you will, is also characterised by control charges, total energy, total electric charge, total environment.
So this is not surprising. Now, what happens if one tracks movement, visual system, for example, to spring pendulum like this one.
It's a oscillate to find efficiencies in all its normal loads and blow things up.
And this opens legal system, but it depends on the system itself.
So for example, for this object here, the idea will disappear.
So obviously it to the mess and of course the local TV stations, it will be not just one frequency, it will be the full spectrum of the spectrum just.
But this can be found and what is crucial to the best of this.
The system itself does not depend on the forces in terms of the system.
It is a intrinsic of systems. So what happens to black holes?
Because to do the same with black holes, I want to return to the cold. I don't want to throw some stuff and it'll make it oscillate.
Give me find the spectrum. What happens if you find the spectrum which characterises black holes and how the spectrum is encoded into this microscope?
So yes,
if you correspondence of biology gives a quantitative way of comparing and studying the spectrum and identifying the ingredients of discrepancies.
So look at the left side of this slide.
So you have some black hole of the brain talk, try to listen to charges and it has done, which is the constant problem entropy.
Now suppose to control that all the original metric is observed by H.M. and his Einsteins equations.
You can write down precise equations which describes these operations h new developments, the properties of the conditions,
the important difference between the normal moles like a bubble and so on, and the black hole oscillations is the presence of the horizon.
Classically, we don't think about qualification like qualification.
Classically, any stuff that shows inside the present disappears forever.
And therefore our system is not a normal mode system anymore because information part of information of the system is lost.
Once the quantum device, you can think of some quantum, but well for example Reddington as well.
So constant walls and parking of information which not so simple as the horizon, but the dimension will not.
So the spectrum will not be real in this case, it will reflect the fact that a very the problem is on the mission.
It is known as the normal spectrum. It will acquire some zero imaginary.
But this is exactly the same. What happened is the digital.
This is the same as happens. If you take the usual no gravitational system and deviate from equilibrium, what will happen?
Give it from within. A system most likely to interact will be some diffusion of it will be Soundwave for example, right?
If in return the air in this room some more important offers will be absolutely.
The something will not propagate, for it will actually it will die.
Eventually it will die because the dispersion relation from is only has an optical emission.
The reverse version of the discourse. We see the resurrection here and here is this first relation of a sound.
You can see the part that describes the propagation of sound.
And then there is a creation part which is proportional to the viscosity integration.
So from this in the slide, it is clear that if you identify the microscopic system which describes all the whole, we must find the quantity.
The condition is in question almost spectrum of black holes and the spectrum of microscopic system, and this has been done.
So one simple example is the following. This is the spectrum of the black hole, the honest completion from from from the official site.
And this is the expression of relation which is expected from the point of view of the fuel theory practice, which is pretty.
So I compare the two, you can see that the speed of sound is still the flight going by the School of Free.
And you can compare these two terms and leads of the ratio, distortions of the ratio.
I don't want to just mention this. Moreover, one people and the relation of just spoke situations of this fluid of the spectrum.
So the beauties of freedom and I size equations want to take this has done around 2007 2000 custody.
So this is very recent stuff. All right.
Coming to the end. So we have some black holes.
Both. You also believe this makes all Jews from the first point of view of this,
the destitute of knowledge, any decent credit for if you really must be able to explain the problems.
This is not left for liberals offensively.
A double helix, I think.
You know why? Because we talk about the principles. We know that in some models, in some cases,
we are able to identify but decided to be the political to guard the behaviour of the whole little spectrum of conservation.
Some call it non-equilibrium properties of this will because viscosity,
like in many other problems, we do not know how to resolve the black similarity.
This is a puzzle with us for many, many years. This is like smoking, breaking.
I sense there is an approximation if you remember this analogy, just in case we do not know the whole theory at the global level.
This is what's frustrating and it's also interesting, and we should also not forget the first publication,
because all this stuff was about the theoretical concept of We're hopeful but realised.
The problem is often the theoretical form, the fuel. But we should not forget about practical applications and real black holes, for example,
real black holes in our very own universe and quite a lot of damage to see the next level inside these real black holes.