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They did not think it over. So the legal discussion about polls in 1970 and beyond the outlying peaceful
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and personal reminders of intensity and vigilante response time by people,
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opinions and rhetoric. We'll talk about quantifying this relationship.
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And that brings us suppose.
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Then we'll discuss the most fundamental solutions of general relativity, such as washing, first, personal notes, the tests on human efforts.
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And then we'll come to political discussion of that crisis discussed in this article versus course, the literature.
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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.
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But whole entropy then will come more smoothly to focus such as holographic principle, which you.
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So first of all, we all go to some extent some people from high school, some people from popular movies,
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or else we all know the problems of general relativity, momentum and energy curve spacetime.
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They distort the science. And because of this distortion motion of other questions.
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So exoplanets, libraries around the object that first spacetime change,
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I mean different basically if you have like great synergy and so large quantities of space time,
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the delay train will look up to get slightly more it will be disrupted by the for
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simply the fact that the drug is still in the property will throw things curves.
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So this is the quality to future discussion is over. Quantify this and quantify this.
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We need like old equations before the question to fulfil general relativity or even above 100 years ago.
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And they are Einstein's equations written here and discussing some to behold.
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So basically the context of general relativity is the geometry, which is metric will be affected by energy for mass and vice versa.
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So what are the ingredients of Einstein's equations of motion?
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The main hero of his discussion? The beauty of the magic.
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So let me remind you the simplest facts, such as in front of us,
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we have a two dimensional flat space and it will take the measure difference between points B and C,
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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.
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Then we can take the distances to be small, and then the same line, but no difference.
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And it doesn't. The small elements applies. We have here squared is a small element is equal to x squared plus twice square.
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This is the metric of two dimensional space time.
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We can generalise this for three dimensions. Here squared is equal to the squared white squared plus none of work is that squared.
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If in fact, Weisskopf is contentious with the headlines in the last four or five six dimensions if necessary.
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And so you get dimensional, you get dimensional flat Euclidean spacetime.
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The light element squared is equal to the sample squares.
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Obviously he doesn't want these displacement.
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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.
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He explained the energy where summation over energy is assumed.
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So this example is given equal dimensions.
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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.
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So explicitly this relationship is given here in this line we have four elements already.
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We saw over 83 that are for energy,
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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.
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And we can compare this line to this line and we see that these two of the elements are
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equal to zero and g one is a good one and should have at least in this one as well.
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So this is a metric comes up in fifth dimensional space, so most of which is like this.
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So in the previous example, G was independent of absolute just in metric cost of metric six one and 100,
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but in principle it means about four points in space for this time.
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So for example, we didn't have to name the three dimensional space, the square in which three can use a square.
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But another one important thing. But we can use different coordinates.
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We can use for the same three dimensional space. We can use either official coordinates or circles.
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Origins are shown in this picture, and then the left element will change physically from this.
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Look, it's just not surprising because if we change versions of the discussion with this, the squared will not change.
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But of course these orbits change and therefore the metric itself does a must change.
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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.
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Depends on the point in space why the exclusive dependence on space?
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It will be important to discuss equals.
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So some examples of the metrics here.
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So this is a metric in the field of admissions.
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Now we can generalise this more, and this is the performance of a social media, which is scholarly, getting made by inside and others.
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That's the reaction at least, at least locally in four dimensional spacetime where this is a spatial can't get a squared away.
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Squared is indeed so squared. But the thing is not an independent spectrum.
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They need to put also the time elements into the metric.
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And essentially the cosmos of special relativity is that our spacetime is locally in cost, is beside the dimension given here.
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Again, you can write this metric avoidance, for example, in circle coordinates.
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And again, the same 11 point is two squared squared.
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But this part is written in certain importance. How do we know that our space spacetime is actually current?
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What kind of local experiments and vocalisations can we do to determine the curvature?
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Oh, so it's like this. Well, some people talk about this whole time.
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In particular it goes and then it's actually one of the local experiments is the law is
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that you can draw triangles and try to measure to solve the angles in the triangle.
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You just based on the set, you discover that to some of the angles is equal to 100 degrees.
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If it is not, for example, which handles here,
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you can measure bicycles and discover that the sun exceeds all other places if your space happens to be the cell is one thing,
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this one, but just the charge and then the triangle, the sum of the angles of 300 degrees.
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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,
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the but just the space you can do the whole only you can draw a circle and measurements of
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difference and you discover that in the secondary space discovery is greater than to pay.
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Ah, this is where were in the prestige, which is also price a little bit to measure light elements in fact.
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But what he sees is even less discretion with Weisler downstairs.
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So this is all to Mexico City.
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But then you only ask one. So how do you know for sure if somebody gives me this lecture?
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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
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to partition apartments and actually being the centre for some complicated information back to the flat space is impossible enough.
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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.
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So what will believe that? Explain what this object is. It's the dirty dom so you can only know it is two fold.
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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.
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And this is such a simple domain itself. Depends on the metric.
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So ultimately remote answer is inexpressible in terms of derivatives.
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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.
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So it is a second value, which is called the metric,
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which reminds us of all the human desire you can build other important ingredients such as nature comes up and reach stellar.
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And the important local statement is that the space is slept even only if its human presence is identical as you.
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So you somebody goes to and tries to sell a very complicated poetic statement.
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I found a wonderful solution of Einstein's equation. The space is curved and this is a solution which would be named after me.
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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.
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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.
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And therefore the claim just in this so the even and it's the images will play a very important role in general energy.
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Of course as we saw already you as on the basis of the piece begins in alcohol.
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And here's what I don't think we should send you to the equations.
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You already are. So let us have you. On the left hand side is basically the second order partial differential equations for the metric.
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On the right hand side, there is an object which is known as the stress energy density.
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This encodes energy and matter contained in space.
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So important statement is the following.
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Despite the fact that you don't see any of the images explicitly entering here,
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the equations the oh is this all the previous like the are second order nonlinear coupled
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partial differential equations for the components of achieving you which by the Mexicans.
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Okay, so you can I tries to magically carry the expression of what you're saying is equations of the left hand side.
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So you could see that indeed. The second order of operations and the source of these equations.
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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,
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and he would like to find electrical magnetic field generated by those studies.
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Then write the muscle equations. And these are also partial differential equations with respect to the for potential a new from Amy.
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We can cultivate EMV electrical within the field in more space.
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So the velocity is the same. The electrical magnetic fields here are sourced by distribution of charges of cards.
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Here the method to renew is source by distribution of matter and energy in space.
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There is no fundamental difference in these equations.
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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.
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And people in 19th century did exactly that. However, here I'm saying equations are possible.
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Moving their differential equations. Generic solution is not known.
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It is not unique. It is very, very complicated.
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Set of differential equations. So you are in a similar piece because you decide you will consider zero metric sources supposedly.
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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.
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Situations for theories, which is also a very complicated set of equations and solutions.
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Will you? However, solutions into highly symmetric species can be solved by making assumptions about ultimately, for example,
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if the source is surplus emission, we can assume that the solution will be strictly symmetric as well.
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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.
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Maybe we can make an assumption about the light elements.
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We can think that it will be certainly symmetric.
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That means that the ends A and B here will depend only on the radial distance from the centre,
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but they will not depend on the angles because it is a surplus energy and this is a possible assumption.
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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.
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And you discover so that Moscow Schwarzschild did in 1916.
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You just tell and we'll just all just dishwashers. But one of the most important solutions of journalism.
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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.
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So if you look at the message, it's not so different, different from this.
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I mean, of course, you are breaking similar to this little element here. You jam over a C squared.
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Ha, it does a circle here. If you've got just a zero this vessel, then you're back to the boss dimension.
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This element is actually just these is actually not very large.
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So corrections to this one is very small.
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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.
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How much is based on your skirt? All right, here. I'm sending you, don't you?
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Because what you are and you calculate the selection, what actually will be on the order of total minus nine.
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So it's a rather small distortions based on colour and it's still sufficiently large to affect, for example, justification specifications.
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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.
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What happens? It's a so-called short term reduced and part is equal.
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Each question squared. Then this becomes you and this becomes you as well.
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Therefore this term pulls up. Well, something happens specific and we need to investigate.
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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
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is not is of no consequence is of significance the most object the shortest Regulus is located deep inside the object itself,
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and therefore is not an element of a solution because the solution is on the very top side, but it's from the earth.
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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.
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The shore surface from the British is somewhere deep inside and the solution is hold it outside.
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So you don't, you don't worry about the house inside. There is a different solution that they want you to write inside.
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Inside this inside the solution of the sun, the shortest radius is kilometres.
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And again, this is a tiny, tiny distance deep inside the song.
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You don't worry about the solution there because the solution is very complex.
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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.
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We'll get some political indications from the logic yourself.
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So you remember this piece Inside Dishwasher videos, for example, in the process of the rotation of Pop Superstar.
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Then we got the bullet hole and this is where our problems start.
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So then we have to take the spectacle of this kid celebrities very seriously.
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First of all, you have this well, there's all this events item that are equal to our forces.
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Then this thing becomes zero. And then there's another singularity in the metric, not just scared of you are close to zero.
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Then this whole term goes up and the same happens here. So there's another singularity in the metric that are equal to zero.
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Well, we need to remember that the metric is actually, in terms of issues differently in different partner systems.
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You change the importance of words. And you can think of something here.
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For example, in two dimensions you have the addition words, light elements.
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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.
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Zero. We have a pathology similar to what happens for schedules.
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Right? This whole term does appear historical.
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So but we know that going can make it more automation back to the properties of space and points of origin.
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Zero is no different from any other point in space.
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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.
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So in a similar way,
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we'll get breakfast Russian Federation different board does a couple of things is violence and the vegetable is equal to our s law.
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Population of Baltimore boiling up a little curve.
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However, something will happen as we discuss in the next slide in general to check the story coordinate similarity,
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we need to compute something to see some variation coordinates a change because we need
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something that does not change for the change in system or just a couple of competitions.
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The polar analysers and special variants.
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One of them is called differential variant. It is it is basically a product of three methods of reporting.
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This is support for a first metric.
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This special variance is a version of the one or 2 to 6.
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So this is completely normal people. There are people who are pushing these similar laws up as far as possible.
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So after that, this encourages what we want is a truly nonpartisan letter, an article to see what we don't know.
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We need to modify physics in order to understand what these articles yield.
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But we don't need the money. If I just focus on the central problems that are economical solutions.
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So what happens at such a high speed?
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Something isn't covered. Sadly, the president began to study emotional particles.
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Light rays got all black holes, just like to study the orbits around the star or or any other source.
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So let's think about what comes to light. So curious what happens to special abilities, right?
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The special relativity. If the observer is looking at this here, it's going to be right somewhere in the centre.
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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,
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does not mean in the natural cycle this observer just stays there.
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Then it simply propagates along with that next plane goes up.
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If this particle has some velocity, no matter how small, it will not stay on the same space point.
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It will move in space and therefore it will move on this graph,
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the sum endless flow and the slope will be equal to the speed of the motion of this particle.
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So the maximal speed, the consensus, will be the speed of light.
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And this response to this, they are going to they are going to motion along the surface of the light pole.
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So problems like trains will move in the future along the surface of this well, this small and therefore usually.
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So let's see what happens to problems in the vicinity of the black hole in the centre ties.
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So here are these light poles drawn locally like poles outside of the prison.
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They look more or less like in the special relativity.
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But then you come closer to the horizon with ideas of these, become a little bit squeezed and a little bit delivered.
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This is a property, the virtue of spacetime.
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And then so you can follow these, this, this and a little bit like and the light from this point, for example,
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will only propagate inside the light forms and let them only propagate inside this little,
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little region here which emanates from this from this point.
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But now it's coming through the glass horizon.
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You can see the table, the fish use light bulb to comfort the garden.
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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.
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In here they will only propagate inside this region which is bounded by the event horizon little.
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Never come outside. They can only come inside the inside the size of and eventually they will end up and are
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equal to zero 30 similarities and where we don't know what kind of physics this had.
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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.
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Right. That separates the body is very strong. There's nothing even like the whole scheme just doesn't work.
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So let's see what happens in terms of the more advanced physics and the limits of quantum physics.
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But of course, so again, this is a question magic. And you may ask why?
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So what do we go? Well, this is very genius. The answer is, unfortunately, after a hundred years of Jha, not so much.
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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.
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One thing to remember is that general relativity is an approximate field.
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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,
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but you can easily write down all the terms which are ends and therefore they can handle the action.
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And at one level they must enter the action according to the quantum democracy.
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And if you observe these these until you discover connections between science equations,
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we don't know at the moment what kind of conditions enter these directions.
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But generically we can see but you can actually see are expected.
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So sure. But it does not give us more than a little bit corrections to the message coming from the
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so-called Holy Week first and also coming from quantum quantum groups like Constellations.
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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.
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Compare this again to students.
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Yes, situation describes the motion of essentially any truth, but we know that for a very short distance the fluid is discrete.
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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.
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In fact, you can generalise them.
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Just those equations become closer and closer to this, to this distribution of these molecules and discrete just of fluid.
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So similarly, gravity, if you want, you can think of energy as a simple equation equations.
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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,
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very short distance. We don't know what it is. This is the frontline of the modern particle physics.
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So let's briefly discuss all the solutions of intense equations.
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One of them is relational, not observation. This is a surplus distribution of mass ethanol.
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No charge. Q So look at the metric. It is all the Schwarzschild metric.
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This is an example of this traditional term here, which depends on the charge.
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So now all this ball is, is, is my system is also has an integral charge.
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Q And so we have this term here and this term here.
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It's a good chance to go back to first metric. If not, then it is a generalisation.
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The not just something has to be closely held while the r squared square equation
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will give us the Horizons presence inside the solutions for the extreme solution.
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And it's very important to think theory of issues.
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All right, then another solution is even more important. It will solve by Roy Care in 1963, not so long time ago.
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It is a solution which discussed danger, excellent symmetrical charge, distribution of mass.
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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.
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I'm not going to tell the kind of metric, just notice that is not a solution.
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So you can say while taking charge that the solution will solve.
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So you're going to have to take an absolute symmetric charge.
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Distribution of mass, but only does not completely dislodge just the whole loop in mass charge from the governmental j.
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Now let's go to more advanced topics.
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The portable Civil War games started by Jemmy Carter in 1973, after studying the metrics such as questions, graphics, cards and quantitative graphics.
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But he does support the decision of law that says the horizons of a station in the pool.
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It's also surface take. You can see the surface reality as the analogue concentration of people.
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G nine point basically 4 seconds square. But no, no. Here, look at the eyes of the black flesh.
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That's the kinds of issues important for description of the police.
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The first law tells us, but the valuation sufficient must post the change at best is related to the change of charge.
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At the moment, the change in size is area by default in quantity equation.
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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.
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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.
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It is impossible to achieve zero circles, very focussed costs.
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So what you can do is to compare these four laws of level against the laws of thermodynamics,
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and you find the remarkable, remarkable coincidence if you want.
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Or maybe it's not the constant. So the zero 400 X tells us that the system to solve the problem has a constant
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temperature gene that is very similar to the zero four but negates the first of all,
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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.
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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.
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And the third law says that it's impossible to achieve too much. But if this whole process is just a coincidence, well,
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if you just there's a deeper connection between the laws of platform against the laws of thermodynamics.
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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.
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But it's not clear how in 1972,
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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,
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and was actually lost in very many of the searches because black holes are left with lots
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and lots of information and therefore can also have a temperature associated with them.
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So lot of it is false.
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However, in 1974, Hawking demonstrated that the black holes actually borders on the Asian quantum level and so one in fact associated temperature cut.
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So that was a rather dramatic advance. So here are some formulas.
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So Hawking showed basically black holes can get radiation, a play for you.
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Spectrum of the temperature given by this expression not is the presence of the H bar.
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So it is a process which happens at the normal level.
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And you can see from this formula that the Hawking temperature is inversely proportional to the mass of the black hole.
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So if you have a supermassive black hole, its temperature conduction will be very small.
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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.
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But the temperature will be sufficiently sluggish. So, for example, black hole of one solar masses of hawking.
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So much of the ball is. So this fixes the additional analogy between science conjecture and the baking soda
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entropy estimate is indeed proportional to the kinds of areas in Horizon area,
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and I didn't notice the presence of each far downstairs.
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So that's the immediate consequences and immediate problems which are related to this piece.
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First of all, that whole elaborate the stuff you see from this expression, it's almost obvious that they have negative specific heat.
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Right? So what happens if this is temperature? The black cold is suppose it's released.
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Some of its mass masses decreases masterpieces.
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This end becomes smaller than for a temperature becomes large, right?
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And eventually this black hole will evaporate. The question is what comes after it lies in its liquid.
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The spectrum is completely features. There are no imprints of any information which was ever thrown into a black hole.
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So you can throw you black holes and you start to complicated systems, which some books.
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So although some political systems contain some some obscure information and in the end,
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the windfall of all the irrigation future distribution remains, it seems maybe we don't understand something in the very end of this process.
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But it seems to me this is not just information lost, folks, which has been developed until until until now.
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In fact, it's not going to clear, you know, what is happening then. But that doesn't mean I don't at all.
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The most important question, however, is often what form the microscopic degrees of freedom underlined by most governments?
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Remember, the thermodynamics is also, in effect, your theory. But in the usual systems we have normally microscopic level.
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We go to statistical mechanics, this notion of temperature, entropy and so on, emerging from the dynamics of the microscopic quantum systems.
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So the example of this, the simple example of this is the system of particles, the spin.
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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.
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Then there are more options, Wolf. You just come down for a spin up for four the in the opposite direction so
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that all together in one particle we have to like a states for two particles,
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you know, for microstates.
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Generically, if you have any particles to spin, the number of microstates is equal to the power and and also borders that the entropy,
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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.
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You can easily calculate just proportional to the number of degrees of freedom of this composite.
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What happens? A black hole with all the black holes, entropy, because I'm hoping to calculate the percentages.
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But this entropy looks nothing like the states which we want to count in a similar fashion.
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Maybe to get to get the centre to be in the lack of force can be called to make up this black hole.
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And the problem that we can start talking is what are the microstates?
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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.
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In particular, the strongest one probably is by strange involving 1996,
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we're able to count the microstates of a very special supersymmetric black hole in five dimensions.
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Yeah, it's a far cry from misfortune. Black call since in the middle of our galaxy ensemble.
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But nonetheless it is. It is a model which achieves this success.
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But the result translates exactly the defects that took it from.
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The reason why they had to resort to the special repulsive magic level is the following.
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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.
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You can go to microscopic states of the system, just like in statistical mechanics system of spin.
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Then you squeeze this whole thing beyond this short radius, it becomes a whole and you can get the a sense, I mean,
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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.
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So this is affected by supersymmetry and this other special problems, the bulk of special properties.
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You cannot be sure you hope this is not the case, but they are not serious exactly.
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But this is a major difficulty here. So strong and powerful results is the general life in many ways to find the right physics.
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However, you still do not know how to find the manifestation of the normal level.
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For example, the symbols that hold important dimensions moving less.
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It does profound consequences of relations. Well, let's talk about this.
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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,
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and the entirety of the system will be proportional to the what is this gas such question.
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But notice that because I'm talking entropy,
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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.
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And it seems that the gravitational degrees of freedom in dimensions generically
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are effectively described by some theory you might have some dimensions.
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This is known as the chemical principle, which was first discussed by Fulton Susskind in 1992.
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So again, very clear. This is a great occupied in some way.
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The effective degrees of freedom seems to be of the boundary of this of this region and move over initially.
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So this development resulted in what is known as the eastern gravity,
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sometimes also is known as few correspondence and is basically the same statement.
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And he grew up. It's important to understand the Eastern principle as kind of those who are open of them.
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This. On the calendar.
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So in the open sea creature you have the of grains of low energy and it is the highest described by quantum computing development.
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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.
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Grains of low energy is described by very thin molecules in higher dimensions.
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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.
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The conjecture is that this site is exactly equivalent to decide to do it in a session forward.
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Like, well, the sentiment goes by looks profitable and we don't imagine that the solve.
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So that's all good. So we know that's what I saw.
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But it's a microscopic system that describes all black holes.
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It describes some internal equilibrium because we saw what was a black hole for many stores,
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and therefore these are identified as being cytokines, entropy and temperature.
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But what about black holes beyond the people so uncertain because they're characterised completely by global charges such as mass,
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both electric charge and those forms of momentum.
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And so licensing, if you will, is also characterised by control charges, total energy, total electric charge, total environment.
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So this is not surprising. Now, what happens if one tracks movement, visual system, for example, to spring pendulum like this one.
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It's a oscillate to find efficiencies in all its normal loads and blow things up.
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And this opens legal system, but it depends on the system itself.
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So for example, for this object here, the idea will disappear.
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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.
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But this can be found and what is crucial to the best of this.
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The system itself does not depend on the forces in terms of the system.
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It is a intrinsic of systems. So what happens to black holes?
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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.
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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?
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So yes,
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if you correspondence of biology gives a quantitative way of comparing and studying the spectrum and identifying the ingredients of discrepancies.
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So look at the left side of this slide.
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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.
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Now suppose to control that all the original metric is observed by H.M. and his Einsteins equations.
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You can write down precise equations which describes these operations h new developments, the properties of the conditions,
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the important difference between the normal moles like a bubble and so on, and the black hole oscillations is the presence of the horizon.
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Classically, we don't think about qualification like qualification.
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Classically, any stuff that shows inside the present disappears forever.
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And therefore our system is not a normal mode system anymore because information part of information of the system is lost.
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Once the quantum device, you can think of some quantum, but well for example Reddington as well.
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So constant walls and parking of information which not so simple as the horizon, but the dimension will not.
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So the spectrum will not be real in this case, it will reflect the fact that a very the problem is on the mission.
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It is known as the normal spectrum. It will acquire some zero imaginary.
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But this is exactly the same. What happened is the digital.
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This is the same as happens. If you take the usual no gravitational system and deviate from equilibrium, what will happen?
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Give it from within. A system most likely to interact will be some diffusion of it will be Soundwave for example, right?
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If in return the air in this room some more important offers will be absolutely.
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The something will not propagate, for it will actually it will die.
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Eventually it will die because the dispersion relation from is only has an optical emission.
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The reverse version of the discourse. We see the resurrection here and here is this first relation of a sound.
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You can see the part that describes the propagation of sound.
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And then there is a creation part which is proportional to the viscosity integration.
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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.
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The condition is in question almost spectrum of black holes and the spectrum of microscopic system, and this has been done.
395
00:39:15,500 --> 00:39:24,980
So one simple example is the following. This is the spectrum of the black hole, the honest completion from from from the official site.
396
00:39:25,550 --> 00:39:32,390
And this is the expression of relation which is expected from the point of view of the fuel theory practice, which is pretty.
397
00:39:32,960 --> 00:39:38,440
So I compare the two, you can see that the speed of sound is still the flight going by the School of Free.
398
00:39:38,750 --> 00:39:44,330
And you can compare these two terms and leads of the ratio, distortions of the ratio.
399
00:39:44,660 --> 00:39:52,280
I don't want to just mention this. Moreover, one people and the relation of just spoke situations of this fluid of the spectrum.
400
00:39:52,280 --> 00:39:58,340
So the beauties of freedom and I size equations want to take this has done around 2007 2000 custody.
401
00:39:58,730 --> 00:40:01,800
So this is very recent stuff. All right.
402
00:40:02,060 --> 00:40:06,110
Coming to the end. So we have some black holes.
403
00:40:07,010 --> 00:40:13,250
Both. You also believe this makes all Jews from the first point of view of this,
404
00:40:14,030 --> 00:40:21,260
the destitute of knowledge, any decent credit for if you really must be able to explain the problems.
405
00:40:21,560 --> 00:40:25,140
This is not left for liberals offensively.
406
00:40:25,160 --> 00:40:28,360
A double helix, I think.
407
00:40:28,580 --> 00:40:33,590
You know why? Because we talk about the principles. We know that in some models, in some cases,
408
00:40:33,830 --> 00:40:40,900
we are able to identify but decided to be the political to guard the behaviour of the whole little spectrum of conservation.
409
00:40:40,910 --> 00:40:45,270
Some call it non-equilibrium properties of this will because viscosity,
410
00:40:45,800 --> 00:40:51,440
like in many other problems, we do not know how to resolve the black similarity.
411
00:40:51,590 --> 00:40:56,140
This is a puzzle with us for many, many years. This is like smoking, breaking.
412
00:40:56,720 --> 00:41:06,140
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.
413
00:41:07,220 --> 00:41:16,820
This is what's frustrating and it's also interesting, and we should also not forget the first publication,
414
00:41:16,820 --> 00:41:20,970
because all this stuff was about the theoretical concept of We're hopeful but realised.
415
00:41:21,960 --> 00:41:29,100
The problem is often the theoretical form, the fuel. But we should not forget about practical applications and real black holes, for example,
416
00:41:29,110 --> 00:41:38,390
real black holes in our very own universe and quite a lot of damage to see the next level inside these real black holes.