https://en.wikipedia.org/wiki/Penrose%E2%80%93Hawking_singularity_theorems
The definition of a closed trapped surface is the following: if light is sent from the surface to all directions, then after some time, all the photons are in a "volume" which is smaller than the volume enclosed by the original surface.
A closed trapped surface is, in a sense, a one-way membrane. We argued in our previous blog post that one-way membranes cannot exist because they would break a time symmetry of nature, and break thermodynamics.
We conclude that the assumptions of the Penrose singularity theorems are never met. They are void theorems. The 2020 physics Nobel committee did not realize this.
Can a singularity form in a classical collapse?
Let us ignore quantum mechanics. If we have point masses under the attraction of gravity, can they collapse into a singularity?
Let us assume that we have just two point particles which orbit each other. The particles do not have any other interaction but gravity.
Let us measure energies as seen by a distant observer. The amount of energy of a system is defined by how much a distant observer would receive if the energy were sent to him.
The particles keep orbiting and losing their energy in gravitational radiation. What is the final state?
The gravity charge of the particles grows smaller. There is nothing that would stop the process. A faraway observer sees the system having less and less mass-energy.
Thus, the final state is not a singularity, but a very lighweight system which keeps orbiting and radiating. The particles have to be very close to each other, so that their potential reduces the mass-energy to a low value.
The effect of quantum mechanics
A distant observer sees the particles very lightweight at the end. Does an uncertainty principle prohibit them from coming very close to each other?
A local observer sees the particles still having their original mass. His uncertainty principle allows the particles to come closer than the principle of the distant observer.
Which observer is right?
An equivalence principle suggests that the local observer has the correct view of things.
Anyway, quantum mechanics stops the particles from coming closer. The system has a lowest energy state. In an earlier blog post we suggested that the final state is a "crystal". The lowest energy state of two particles is, in a sense, a crystal.
The Shwarzschild radius or "event horizon" is the place where the "viscosity" of gravity becomes extremely large
We have argued that light can always escape from a black hole. There cannot be a one-way membrane. What is the relevance of an event horizon then?
We get a clue from the Schwarzschild metric just outside the Schwarzschild radius r_s. Light propagates extremely slowly there.
We argued in our October 20, 2021 blog post that a 1 MeV photon can still fall through the event horizon of a solar mass black hole in less than 1.38 milliseconds. Light does not stand completely still.
The event horizon is the radius where the "syrup" of the gravity field becomes extremely viscous. Light moves at a tiny fraction of its normal speed.
We conjecture that light propagates at roughly the same tiny velocity within the event horizon. The viscosity of the syrup is roughly the same inside.
In a syrup, small animals can only move very slowly. But an elephant whose mass is equal to the pool of syrup can still run fast through it.
In gravity, the situation is the same: if we drop a mass M to a black hole whose original mass is M, then the falling mass will move very fast, since it cannot acquire large inertia in the field of the black hole. Small masses will move extremely slowly when they reach the event horizon.
The elephant is another instance of our claim that gravity can create the illusion of "spacetime geometry" for small masses, but not for very large masses. A photon moves very slowly, but a large mass runs through at a large velocity.
Conclusions
There cannot be a singularity inside a black hole. This is true both in classical physics, and in quantum mechanics.
We conjecture that the Einstein-Hilbert action does not lead to singularities, when interpreted correctly. The claim that singularities form comes from the misunderstanding that the geometry of spacetime is "infinitely strong".
Albert Einstein never believed in the existence of black holes, and tried to prove that they cannot form.
In his 1939 paper he claimed that a collapsing system spins so fast that it cannot contract below the Schwarzschild radius.
Now we see that Albert Einstein was on the right track. However, the system does contract below the Schwarzschild radius. But the spinning prevents a central singularity from forming.
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