10 Rotating disc of black hole and Ehrenfest's paradox

  Black holes are unusual in many ways. Thet have also has a spinning disc, a jet, a Schwartzchild radius, a horizon of events and singularities. But there is one thing that can not be explained in modern science or the theory of relativity. It is the rotating disc of a black hole.

Black hole and Ehrenfest paradox

  The speed at which materials rotate in the rotating disk of a black hole is almost as close as the speed of light. If so, all the materials must be decomposed and discarded by the Lorentz contraction. However, the rotating disk of a black hole certainly exists. It is definitely a contradiction. In fact, these are linked to the famous paradox of the Ehrenfest paradox.[1] Today, we will look at the Ehrenfest paradox.

Fig. 1 Paul Ehrenfest

Personally, I think Erlenpest paradox is the best of relativity's paradoxes. Other paradoxes seem to be a little simpler than this paradox.

The list of people who studied this paradox is very extensive. Einstein, Ehrenfest, Max Born, Noether, Planck, etc ... are all very popular people in the scientific community. Einstein was known to have studied this paradox very deeply after he published the theory of special relativity in 1905. In studying the paradox of Ehrenfest, he envisioned general relativity.

Fig. 2 A rotating disc © jacc, Unsplash

The Ehrenfest paradox is about a rotating disc. Let's say we have one disc here. Let's suppose that this disc rotates faster and more or less at relativistic speed. So what happens? There are two problems with this.

1. The disc is broken by the Lorentz contraction.

2. The circumference of the rotating disc is smaller. If you fill a gap with the same size, it is longer.

(Today, I'm going to focus on this first question.) First, Ehrenfest proposed this thinking- experiment and assumed an ideal rigid body. It is an object without deformation under any circumstances. In reality, however, it is the first challenge of this paradox that these objects are theoretically impossible. In fact, we anticipated these problems even before objects that run at relativistic speeds were found.

We assume a rigid body, but for purely theoretical reasons, this rigid body will be ruptured and separated during rotation. The cause is centrifugal force and Lorentz contraction. Since we assume a rotating disc, as the speed of the disc increases, the disc becomes inevitably separated as the speed increases.

Fig. 3 Rupture of rotating disk due to Lorentz contraction

We have assumed an ideal body that should never be ruptured, but it must be ruptured by the Lorentz contraction. This is a paradox.

Finally discovered Ehenfest disc

   Surprisingly, objects rotating at almost the speed of light were not found in thinking experiments, but were found in the real world. It is a rotating disc of neutron stars and black holes. As you were worried about the first time, you do not have to worry about rupture of the disk due to centrifugal force. The reason is that the gravity of the black hole corresponding to centripetal force is extremely strong. Only Lorentz contraction is sufficient. These particles of disc are not decomposed and actually exist as celestial bodies. If it is according to Ehrenfest's point of view, the rotating disc of such a black hole should never exist.

However, these objects are actually found in space. The rotating disk of the black hole in the center of the galaxy NGC 1365 is rotating at a speed of 0.84c of light speed. Below is the content. 

How Fast Do Black Holes Spin?

If the rotational speed is 0.84c, the Lorentz factor γ is almost 2. At this level, all of the particles we know, such as molecules, atoms, protons, neutrons, and mesons, must be decomposed and destroyed by Lorentz contraction and the gap created by them. If all of the materials are decomposed, no x-rays are found around the black hole. However, there is still a rotating disc of black holes in the sky. How do you explain this phenomenon?

The secret of the rotating disk of a black hole is released

Now, let's solve this problem. Explaining this with length expansion makes this paradox easy to explain. First of all, in terms of length contraction theory, the overlap of orbital is reduced, as shown in figure (b) above. So, in the end all the bonds are broken down. However, the situation is somewhat different from the length expansion theory. Let's take a look at only two orbitals. The figure below shows (d).

If you place multiple orbits in a circle instead of two orbits, you can see below.

  If the length of the orbitals is increased even if the disk is formed, the overlap of the orbitals increases as well, so there is no degradation. If this is true, even if the black hole is rotated close to the light beam, the material will not be decomposed. Then, the first problem of the Erlenmeyer paradox is solved.

The theory of length contraction can not explain the existence of a rotating disk of a black hole rotating at 0.84c at the center of NGC 1365, but the theory of length expansion can be explained rather easily.

"The relativistic theory of length contraction cannot explain the existence of a rotating disc of a black hole, but the relativistic theory of length expansion can naturally explain the existence of existence."

Once again, Erlenfest issues the following issues:

1. The rotating disk, assuming an ideal rigid body, is broken (actually, an object rotating at a relative speed was found, but there was no decomposition of the material).

2. The radius of the disc is always perpendicular to the direction of motion. However, the circumference of the disk when it is stationary and the circumference of the disk when rotating are different from each other. This is a contradiction.

Today, we looked at the first of these. The first problem is solved. The second problem will be posted later. The second problem is also relatively easy to solve, assuming that the radius of the disk does not change in the assumption of the Ehrenfest paradox. To conclude, there is no such thing as the bending of space, and the length of the circumference is the same as when it is stationary and when it is running fast. With length expansion theory and a few facts, everything is clear.