0:13

So, we want to complete, finish our discussion of the black hole

Â like solutions in general theory of relativity with a discussion of

Â another very complicated and subject on which there is no generally,

Â commonly accepted opinion in the scientific community.

Â So let me phrase the problem that I want to address.

Â We have obtained the following Penrose diagram describing the collapse process.

Â 1:05

So, this is the region which is inside the star, in the body of the star.

Â So consider some observer which stays always outside of the star.

Â It's world line is like this.

Â So from the point of view of this observer, the collapse is never ending so

Â the surface, the last light ray which is emitted or

Â refracted by the star goes along the horizon, and

Â reaches the observer only at its future infinity.

Â 1:40

We have seen this effect in many different situations, in many different

Â calculations, that body which is falling inside a black hole, it takes from

Â the point of view outside observer, it takes infinite time, etc., etc.

Â So there are different ways to see this phenomenon.

Â So then appears a very obvious question.

Â Well, of course, there is always event horizon, for

Â the collapsed process there is an event horizon.

Â This event horizon is present there always.

Â But the question is whether the black hole from the point of view, the matter,

Â the body of the black hole, the matter which creates a black hole.

Â The point is if from the point of view of the observer which stays

Â always outside of the black hole, the question is

Â whether this creation happens during finite period of time or not.

Â 2:36

You see that we observe the following situation that basically,

Â the matter which contributes to the black hole from the point of view of

Â outside observer always eternally stays outside of the horizon.

Â It never crosses this.

Â So, I want to establish a few things.

Â First of all, I want to clearly state the approximation

Â in which this statement is valid, and

Â then I want to propose my not generally accepted opinion on what is going on.

Â I want to convince you that the creation of

Â the black hole happens within finite time even from the point of

Â view of those who are staying eternally outside of the black hole.

Â Why?

Â The reason is the following.

Â This statement, so suppose we have a star which is collapsing, and suppose

Â 3:49

One may say, why address this question because this radiation experience

Â is exponential red shift.

Â The frequency experienced is exponential red shift.

Â So there will be no device which is capable to detect this phenomenon.

Â But you see this exponential factor is crucial for

Â many phenomena that are happening in the black hole.

Â For example, this exponential factor is crucial for the Hawking radiation.

Â So, due to this exponential factor we have the Hawking radiation.

Â Of course, one may say that there is no device which can detect this but

Â the Hawking radiation is exactly due to this factor.

Â So, I think that the discussion I am conducting is important to

Â understand deeper the Hawking radiation and the back reaction on it.

Â So that's the reason I am discussing this phenomenon.

Â Again, there is radiation which is refracted or

Â emitted by the body of the star and detected by this guy.

Â The fact that this radiation, how you call it,

Â if it is emitted in equal periods of time is reached by

Â observer but the time is increased.

Â So the periods, these are periods becoming bigger while these are fixed.

Â That can be seen from different ways of calculations and

Â is related to the fact that the time slows down as from the point of view

Â of this observer, every process on the star surface slows down.

Â But this statement is obtained in the following approximation.

Â In the approximation that light rays are going along light-like geodesics.

Â 5:52

that light ray carries energy and also curved spacetime.

Â So basically this spacetime is described the following observation

Â that it is curved by the black hole but

Â we neglect the fact that it is curved by the observer or by light rays.

Â The question is whether this neglection is meaningful

Â when we discuss such an exponentially suppressed phenomena.

Â 6:18

And I'm trying to explain to you that it is in fact,

Â important to take into account the fact that light rays are also

Â bending, curving the spacetime because they're carrying energy.

Â And if we take into account the fact that light rays also are contributing to

Â the curvature of the spacetime, the process looks a bit different.

Â Let me clarify this point on the picture that we have described

Â in the lecture four.

Â In that lecture where we have obtained for the first time Schwarzer's solution.

Â In that lecture, we considered that

Â the light-like geodesics

Â in the Eddingtonâ€“Finkelstein coordinates.

Â So there was a peculiar, so this is, let me tell,

Â say that this is a singularity r = 0, this is r = rg.

Â And then we had the full length picture.

Â We had outgoing light rays behaving like this.

Â 8:12

Of course, if a light ray carries energy, if we take into account that it

Â carries energy and also curved space time, it goes along the curve which is

Â actual light-like line, world line rather than geodesic which is for

Â the small energy carried by light ray is a little bit different from this guy.

Â So, those will be a little bit different.

Â Of course, this picture is not applicable anymore in that circumstances

Â because in this case, the picture is stationary, so

Â it repeats itself at every different moments of time.

Â It's stationary, while if we take into account that the fact that light rays also

Â carry energy and curved spacetime, the situation becomes nonstationary.

Â But approximately for short periods of time, for short period of time,

Â if we discuss only seeds of light rays, seeds of light rays, in that case,

Â we can we have a very similar picture, very similar picture.

Â But light rays are a bit, actual light rays are a bit different

Â from the geodesics, a little bit different from the geodesics.

Â But now what do we encounter?

Â In the original picture for the geodesics,

Â we had the following situation that this vertical line, this vertical line which

Â corresponds to the horizon here was also one of the light rays.

Â So if a light ray was standing on this line,

Â eternally stand on it, eternally go along it.

Â 9:46

But if we take into account the fact that light rays also carry energy and

Â bent, curved spacetime, the picture will be similar.

Â We will also have a family of outgoing geodesics that are in this

Â region are going to infinity, in this region are going inside,

Â in the seeds we will see that.

Â For the seeds, this will be apparent.

Â But it will happen that this light ray will either belong to this family,

Â or to this family, but will not eternally stay on this surface,

Â due to the fact that it also bend to curved spacetime.

Â So, it will contribute to the emission of gravitational waves or

Â some other stuff like that.

Â So, let me re-phrase this what I am saying in different terms,

Â I'm saying the following thing.

Â That if this guy emits radiation which is received by

Â an absorber which stays always outside the black hole,

Â this absorber will see the very last sug,

Â the very last wave packet emitted by the star.

Â And the one which is after it will contribute to the body of the black hole

Â to the energy of the black hole, and will not be received by this observer.

Â So this observer will stop receiving light rays from the collapsing body.

Â Will stop receiving light rays from the collapsing body within finite

Â time as measured by this outside observer.

Â So, this moment can be considered as the moment of the creation of the black hole.

Â Of course, this explanation that I have gave to you,

Â has some drawback because the moment of the creation of the black

Â hole is somehow related to the energy carried by this light ray.

Â Stronger is the energy carried by each wave packet,

Â earlier the creation is happening.

Â This is a drawback.

Â And of course, I am vaguely explaining to you the picture

Â which demands some farther regress study, an explanation.

Â So I just gave you the idea, my idea of what is going on and

Â why the creation of the black hole happens within finite period

Â of time from the point of view of outside observers.

Â [MUSIC]

Â