# Scientific interstellar: how to fall into a black hole and why Hawking could be wrong

### How space-time behaves next to a star

To understand what a black hole is, you need

to establish how space-time bends. My task is to draw a coordinate grid inspace-time, for this I use imaginary lines like meridians and parallels on the surface of the Earth. You can draw the same map in space-time: first without a black hole, and then in its presence. For this I will use rays of light. The reason is as follows, and this has been known since the time of Heron of Alexandria: light moves along a trajectory with the least amount of time. Using this principle, you can, for example, calculate the refractive indices, or rather, knowing the refractive indices, you can calculate how light will be distorted when it goes from glass to air or from water to air. If the properties of the medium do not change, the light moves along the shortest path.

An example of a homogeneous space is a vacuum: a void in which there are no particles. The light in it, according to Fermat's principle, must movealong the shortest path. If light moves in flat space, that is, in two-dimensional and non-curved space, the shortest path will be a straight line. But it turns out that in the presence of gravitating objects, light does not move in a straight line: the rays of light are bent. This is due to the fact that gravitating bodies bend space-time.

In Newtonian mechanics, distance in space is measured separately and time is separately measured. Why do we need it?To, for example, determine the flight path of a particle, nucleus, rocket or plane. The special theory of relativity states that there is no separate way to measure distance and time, but there is a single way to measure distances in space-time. When we talk about the space-time continuum, we are talking about four-dimensional space: three coordinates plus a time coordinate. But it is not very clear how to draw a four-dimensional space-time on a two-dimensional surface. We know that position in space can be determined by three coordinates: x, y, z are Cartesian coordinates. On the other hand, we can accurately determine the position of a point in space using spherical coordinates. Therefore, only the r coordinate and the time coordinate can be used. The result is a half-plane, because r is always greater than 0, and time can be from minus to plus infinity. The point in this space is this sphere. For example, at the moment of time t0, if I consider the point r0 on this half-plane, then it is just some sphere of radius r0 taken at the moment of time t0.

There is a sphere of radius r0, and from any point of this sphere rays of light are emitted, going inward and outward. That is, a wave front of light is obtained that goes inward - a contracting sphere, and going outward - an expanding sphere. But imagine that at any given moment the space is stratified

like an onion.At the moment of time t0, a sphere of radius r0 is taken, from the surface of which the rays emanate. Those that go inward form a front with a radius r0 - Δr, and those that go outward - r0 + Δr. The slope of these lines with respect to the vertical axis is 45 degrees, because the speed of propagation is equal to the speed of light.

If we are dealing with a particle thatdoes not propagate at the speed of light, then it cannot move at a speed greater than the speed of light, and, accordingly, can move in any direction within this angle.

.If we draw imaginary rays of light using our diagram, we get an imaginary grid. From this figure it is clear why I chose the raysSveta. Imagine that instead of light, I would choose some other particles that have mass, then an ambiguity would appear in the coordinate grid: particles can move with any speed. Why is light beneficial? The fact that there is an ambiguous choice in the direction: either outward or inward, and after that the grid is unambiguously fixed.

How does the presence of a star change radiation? Imagine that there is a star with a radiusbody -body. This means that it fills all the radii up to the body, because there is some substance inside. At a given moment in time - for example, t = 0 - the star looks just like a segment. If you consider all the moments in time, you get a strip. Now let's imagine what will happen to the rays of light in the presence of a gravitating body. Rays of light are drawn in red, as they would look in the absence of a star. And violet - rays of light in the presence of a gravitating body. From general considerations, several conclusions can be drawn: the gravitating body distorts the rays of light, and those rays that are closer to the star are distorted more than those that are farther away. Therefore, far from the star, violet rays practically do not differ from red ones.

Imagine that the mass of the body begins to change, and the radius is fixed. The mass will grow, and the more it is, the strongerthe body will influence the rays. At some point, the mass will increase so much that the following phenomenon will occur. At some point, some corner will be on the priest, that is, just vertically. I took the point of emission of violet rays not at the radius of the horizon, but slightly inside, so the ray does not go vertically, but is distorted.

At the moment, there is no limit to the increase in the mass of a black hole. At least we don't know. Perhaps the point is that anynatural science theory has limits of applicability, which means, in particular, the theory of relativity loses its applicability somewhere in the inside of a black hole. General relativity loses its applicability very close to the region where almost all the mass of a black hole is concentrated. But at what radius this happens and what replaces the general theory of relativity is unknown. It also cannot be ruled out that if the mass of the black hole increases very much, something will change.

The first question that should arise is: where did the star go? Since the trajectory of any particle with mass canto be only inside this corner, it moves like this (red - "Hi-tech") and gets to the center. If from any point a particle with a mass will inevitably fall into the center, then the entire mass, the entire body of the star will be compressed to the center.

The problem is that the r and ct coordinates are only applicable in a certain area, and outside of it no longer. Imagine what you have on the surface of the Earththere are meridians and parallels, and with their help you can find the position of any object. But on the surface there is a cave that goes deeper, and the task is to determine the position of the fly in this cave. Longitude and latitude are no longer suitable for this, now you need to enter a new coordinate grid. There is some substitution: I drew a picture using r and t to show the phenomenon, but it is important that there are no longer coordinates r and t, but there are some other coordinates that describe the behavior inside the black hole. This means that there time is not directed vertically, but flows towards the axis, and this is shown by these corners.

To get a coordinate grid for the space-time of a black hole, you can take a static picture and repeat one after another, "gluing" one to the other. Outgoing rays are drawn in purple, andred - entering inside. A vertical ray is also a ray of light, r of the horizon. These purple lines are divided into two groups. Those that are directed outward go to infinity, and those that are inside are directed inward and go to r equal to 0. This phenomenon is a black hole.

### What happens to an object when it falls into a black hole

Imagine that an object is hanging over a black hole, and its clock is ticking, or the object flew to the black hole and returned, and its clock was also ticking. I can tell how much has flown by the houreach of these objects. I'll just calculate the length of the line he drew on this diagram and divide it by the speed of light. The one that was hanging, it beats at one time, and at a flying one another. For example, one may take several hours, while another may take years. Like in the movie Interstellar. We see a similar phenomenon on Earth, but it does not distort space-time so much. This is noticeable in global positioning systems: the clocks on satellites that participate in the global positioning system show a different time. If I fly to the satellite and return, the time on my watch is different from the satellite. This phenomenon is taken into account in order for the GPS to work.

According to the watch of an observer who is hanging over a black hole, an infinitely long time passes while he observes an object falling into a black hole. An object that falls into a black hole is nevercrosses the event horizon. He is getting closer and closer, like Achilles behind a turtle, but he can reach him. The end time will pass according to the object's clock. How to determine this? Measure the length of the world line between the same parallels and meridians. The longer this segment, the more it is curved. The object flies, time intervals tick on its clock - on the graph these are parallels that are spaced along the world line at equal time intervals Δt. But where the observer is, the time interval grows, and as the event horizon approaches, the time interval grows indefinitely. The moment an object crosses the black hole's event horizon, an imaginary ray of light travels vertically along the horizon and never crosses this line. Therefore, the observer will never see the moment of intersection, and from the point of view of the falling object, a finite number of time intervals pass. This phenomenon looks mystical, but when they say that time flows in different ways. This is not entirely correct. Time does not slow down, the object does not move slower. Time was ticking and ticking, just by my watch, one thing is ticking, by someone else's clock - another.

In Interstellar, there is a moment when the main character fell into a black hole. As I understand it, he flew to the center, and he was nottore apart. While it was falling, it flew close to this accretionary matter, the accretion disk, which we see, and as I understand it, it emits in a hard X-ray range. The hero of the film still received this radiation, and, probably, quite strong. He, firstly, was irradiated, and secondly, from the point of view of his comrades who are outside, he flew for an infinitely long time. But in fact, it falls over a finite time. And then he hit the center and was not torn apart. Film consultant, physicist Kip Thorne proceeds from the fact that we do not know what is happening under the event horizon, which means that there could be anything, for example, a fifth-dimensional world.

### Could a collider spawn a black hole? The opposite has not been proven!

In 2008, many heard of the physicist Rossler, who was actively trying to shut down the Large Hadron Collider. He even tried to sue the German government.It was a really serious risk, because he could win in court, which means that 10% of CERN's budget could simply disappear. But CERN also turned its back on Rossler, and the director of the Max Planck Institute once said that this should not be left to chance and that we need to talk to Rosler. Moreover, this scientist is one of the qualified matphysicists. He even has a non-linear attractor that bears his name. He cited a funny fact as a counterargument against the LHC. That cosmic rays have higher energies than at CERN. Therefore, something there on the Earth will shandarah, and maybe a black hole will form, but it flies out of the planet with great speed and flies away somewhere, so we do not see it. But not everything happens in the center of mass, therefore, in a collision there, on the Earth, a black hole may remain, it will sit there and quietly devour us. The director of the Albert Einstein Institute gathered several people, including me, and we had to "choke" this Rossler and convince him that he was wrong. However, he did not go to court.

The theory predicts that this black hole, which could be formed as a result of a collision in the collider, will immediately disintegrate. Since it is very microscopic, it willvery intensely emitting according to Hawking and decays quickly. Rossler said Hawking was a fool and wrong. The hole will sit there and eat, another thing is that it was small, so it can only eat what is smaller than its size, but this also takes some time. She must first eat something small, then slowly grow, then larger, and so on. And this strategy of talking really seemed to be winning, especially in court. We do not rule out that a black hole will nevertheless form, that Hawking is wrong and it will not disintegrate. We haven't really tested anything experimentally. These are all theoretical discussions only.