How space-time behaves next to a star
To understand what a black hole is, you need
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, two-dimensional and uncurved, 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 this?To, for example, determine the flight path of a particle, nucleus, rocket or aircraft. 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 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 the time can be from minus to plus infinity. A point in this space is this sphere. For example, at time t0, if I consider a point r0 on this half-plane, then it is simply some kind of sphere of radius r0, taken at time t0.
There is a sphere of radius r0,and from any point of this sphere rays of light are emitted, going in and out.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 time t0, a sphere of radius r0 is taken, from the surface of which rays emanate. Those that go inward form a front with a radius r0 - Δr, and those that go outward form a front with radius r0 + Δr. The inclination of these lines relative 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.This picture makes it clear why I chose 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 at any speed. What are the benefits of light? Because 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?Let's imagine that there is a star withradius of the body rbody. This means that it fills all the radii up to the rbody, because there is some substance inside there. At a given moment in time - for example, t = 0 - the star looks simply like a segment. If you consider all points in time, you get a strip. Now let's imagine what will happen to rays of light in the presence of a gravitating body. The rays of light are drawn in red as they would look in the absence of the star. And violet - rays of light in the presence of a gravitating body. From general considerations, several conclusions can be drawn: a gravitating body distorts light rays, and those rays that are closer to the star are distorted more strongly than those that are further away. Therefore, far from the star, violet rays are practically no different from red ones.
Imagine that the mass of the body will begin to change, and the radius will be fixed.The mass will grow, and the larger 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 its butt, that is, simply vertical. I took the point of emission of violet rays not at the radius of the horizon, but slightly inside, so the beam does not go vertically, but is distorted.
At the moment, there are no limits to the increase in the mass of a black hole. At least we don't know.Perhaps the point is that anya natural science theory has limits of applicability, which means that, in particular, the theory of relativity loses its applicability somewhere inside a black hole. General relativity loses its applicability very close to the region where almost all the black hole's mass 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 canbe only inside this corner, it moves like this (red color - “High-Tech”) and hits the center. If a particle with mass inevitably hits the center from any point, then the entire mass, the entire body of the star, will be compressed into the center.
The problem is that the r and ct coordinates are only applicable in a certain area, and beyond that they are no longer applicable.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 - those entering inside. A vertical ray is also a ray of light, the horizon. These purple lines are divided into two groups. Those that are directed outward go to infinity, and those that 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 time has passed by the clockeach of these objects. I'll just calculate the length of the line he drew on this diagram and divide by the speed of light. The one that was hanging is moving at one time, and the flying one is running at another time. For example, for one it may take several hours, while for another it may take years. Like in the movie Interstellar. We see a similar phenomenon on Earth, but it does not bend 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 a satellite and return, my watch displays a different time from the satellite. This phenomenon is taken into account in order for 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 nevercrosses the event horizon. He is getting closer and closer, like Achilles behind the tortoise, but he can reach it. According to the object's clock, the final time will pass. How to determine this? Measure the length of the world line between equal parallels and meridians. The longer this segment, the more curved it is. The object is flying, time intervals are ticking on its clock - on the graph these are parallels that are spaced along the world line by equal time intervals Δt. But where the observer is, the time interval grows, and as one approaches the event horizon, the time interval grows without limit. At the moment when an object crosses the event horizon of a black hole, 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 begin to move slower. Time was ticking and ticking, it’s just that according to my watch one thing is ticking, and according to other people’s watches something else is ticking.
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 was nottore apart. While it was falling, it flew close to this accretion matter, the accretion disk, which we see, and as I understand it, it emits in the hard X-ray range. The hero of the film nevertheless received this radiation, and probably quite strong. Firstly, he was irradiated, and secondly, from the point of view of his comrades who were outside, he flew for an infinitely long time. But in reality it falls within a finite time. And then it hit the center without being torn apart. The film's consultant, physicist Kip Thorne, proceeds from the fact that we do not know what is happening under the event horizon, which means 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.This 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 away from Rosler, and the director of the Max Planck Institute once said that this should not be left to chance and that it was necessary to talk with Rosler. Moreover, this scientist is a qualified one, a mathematical physicist. He even has a nonlinear 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 will crash across the Earth, and maybe a black hole will form, but it flies out of the planet at great speed and flies away somewhere, so we don’t see it. But not everything happens at the center of mass, so in the event of a collision, a black hole may remain there on Earth, it will sit there and little by little devour us. The director of the Albert Einstein Institute gathered several people, including me, and we had to “strangle” 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 willemit very intensely according to Hawking and will decay quickly. Rossler said that 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 it, but this also takes some time. It should first eat something small, then slowly grow, then larger, and so on. And this conversation strategy really seemed to be winning, especially in court. We do not rule out that a black hole still forms, that Hawking is wrong and that it does not decay. We haven't really tested anything experimentally. These are all just theoretical discussions.
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