On the size of black holes "on the fingers"

Today we do not know for sure what is happening under the surface (in the sense, beyond the Event Horizon) of a black hole. We can only guess and guess. Since direct observation of the interior of a black hole is inaccessible to us today (or it may happen that it will never be available), the most sure thing that remains for us is to take the best theory that exists today, and try to predict what is inside a black hole in general. take place.

The best theory, in which we are more or less confident (because it is confirmed by direct observations), on a cosmic scale is Einstein's Theory of Relativity. As they say, this is not the best, that is the best, but as long as it is the best of what we have.

Black holes themselves, like wormholes of space-time, were just theoretically predicted at the beginning in the Theory of Relativity, and only many decades later we began to observe them in reality.

Therefore, to study (and in fact, reasoned theorizing) of the structure of the interiors of black holes, Einstein himself ordered the use of the mathematics of the Theory of Relativity (TO), as long as this is the best that we can neeorize, assuming that since the other conclusions of TO are confirmed by observations, then these, too, can be more or less relied upon.

According to the Theory of Relativity, space is a smooth space-time, in some places curved by the presence of matter in space (energy-momentum tensor). Black holes make a particularly perverted perturbation with space-time, they do not just bend, but actually tear space-time to shreds, from which it is more convenient to use Cartesian coordinates, which are not familiar to us, which everyone studied in the fifth class, and the so-called. coordinates (or diagram) of Kruskal.

The Kruskal diagram is not so complicated, but still a decent matan, this is clearly seen in the English version of Wikipedia, from which I immediately propose to go to its simplified version, the so-called. Penrose diagram, which is essentially the same thing (even visually, the similarity is noticeable), only there are fewer extra lines.

In order not to blow up unprepared minds, only the right half of this diagram is usually shown to the general public, because people begin to get excited and react inadequately to the words "Parallel Universe", "White Hole" and so on.

The Penrose diagram says that space-time in the Universe can and should be divided into two parts, a part where we are, our Universe, and a part that is inside the Black Hole. There is not quite our Universe, more precisely, there is a part of our Universe, in which space-time does not behave the way we are used to. These two parts are separated by the edge of the Event Horizon (Horizon), and in the picture you can see that this border is one-sided, you can go inside (there is an arrow drawn there), but there is no way back.

This happens because, strictly speaking, the boundary of the Event Horizon does not divide space-time into two parts - inside and outside. It is the junction (scientists say "the place of gluing") of two completely different space-times.

Fundamentally different.

If we take the formulas of the Theory of Relativity, and begin to solve them in space-time, which is in our Universe (above the Event Horizon, that is, in quadrant I, where there is a diamond with the inscription Universe), then we get the familiar three coordinates of space and one coordinate time. Which somehow change there, bend depending on the presence of mass, but more or less in the usual framework.

And if we start solving the same formulas, but at the same time we will be inside a black hole (under the Event Horizon, in Quandrant II, inside a triangle with one side of the saw without biting), then all decisions will tell us - dudes, you have space and time have reversed!

It turns out that in those places where we expect to meet our familiar spatial coordinates x, y and z, the time coordinate t suddenly begins to creep out and vice versa, where we are waiting for changes along the time axis, x, y and z, or rather their derivatives, suddenly appear, although by and large, in our case it is the same thing. That is, you can take courage and say: "Space has become time, and time has become space!"

NB! Attention, the author categorically does not recommend saying so out loud! This is not entirely true, or rather not at all true. Time does not become space in fact, just the formulas begin to indicate that something like this is happening.

It turns out that space acquires properties that we previously associated with time, and time, to some extent, is endowed with the properties of space.

For example, everyone knows that we have three coordinates of space, as it were, "free", we can move along them in any direction, but the coordinate of time clearly points forward, and whether you want it or not, you can only move along it where the arrow points, that is, from the past to the future.

Inside a black hole, space-time is arranged in such a way that you cannot move where you want. You can only move towards the center, towards the singularity. Which in this representation turns out not to be the usual point, but as a line, and even specially drawn with a bloodthirsty-jagged line to show an unwary traveler who has gathered instead of Turkey to rest in a black hole - "there is the end, there will be eaten." The singularity of a black hole is inevitable (in this case, by the way, this is not a pun at all), as the future is inevitable for us, because it is in the spatial future, that is, the inevitable fate of any object that has fallen into a black hole is to find itself in a singularity. Wherever you move, in whatever direction you try to fly - all the same, space will carry you exactly to the singularity.

That is why, by the way, it is impossible to get out of a black hole. Not because it "attracts so strongly, " although that, of course, is also. And because, just like in our usual life, no matter what you do, wherever you move, you still will not get into the past, and the future cannot be avoided, so in a black hole - all roads lead only to a singularity, back to the past, there is no longer a path to the ordinary Universe.

At the same time, it turns out the opposite thing, which I actually put into the post. Theoretically, time has no limit, the future stretches to infinity. Well, that is, yes, the life time of our particular Universe is most likely not infinite, Thermal Death (or even a Big Rip) awaits it, but if we abstract, we can move into the future indefinitely, even with the Thermal Death of the Universe, time will not stop, just in in space, visible processes will cease to occur, from which one moment of time will become indistinguishable from another, but this is already the beginning of sophistry, in any case, this is still a very, very, very, very long and far away.

The black hole is also not eternal, because of Hawking's radiation, it should, like, slowly evaporate. But this is a very, very slow process, a black hole with a mass in the Sun will evaporate ~ 1066 years (do not forget that the age of the Universe is only ~ 1010 years!) From which, with a certain amount of imagination and simplification, one can declare that the size of a black hole stellar magnitude from the inside is at least 1066 light years, which inside it, if not infinitely large, then at least 1000000000000000000000000000000000000000000000000000 times the size of the Observable Universe.

Well, one more time. Naturally, all this is still just idle reasoning and theorization. What really happens inside the black hole, we do not know. I will say more, we know for sure that there is most likely not quite what we can nateorize today, the Theory of Relativity is not complete, so that it works in black holes for sure, it definitely needs to be married to quantum mechanics, and this, for almost a century, cannot be done by anyone. From which reality is likely to turn out to be even more complex and confused thing than we think and argue today.