m falling in
• --> ● ----> extreme acceleration
M frozen star
In the Minkowski & newtonian model, the gravity force, measured in the canonical coordinates of Minkowski space, is not infinite close to the event horizon. The force is only "reasonably" strong, like that of the newtonian gravity force of M, or some small multiple of that.
The inertia of the test mass m resists the acceleration of m along with M. How big is the inertia of m in this case?
Let us pull the system M & m with a large force F. What is the inertia of m in this operation? We assume that m fell from a large distance close to the event horizon of M. A reasonable guess is that the inertia of m is simply m.
Thus, if we accelerate M fast enough, then m in the accelerating frame of M will feel a force to the left. The test mass m has a very large inertia when it is close to the horizon. The test mass m will slowly climb up, so tht its distance from M grows. Essentially, this is the reverse of the descent of m toward the horizon of M.
We showed that we are able to lift a falling mass m up from the horizon of M. We can then iterate this process and disassemble M by pulling eventually all particles up from M.
Though, in practice, we are unable to perform the disassembling. It would require a huge acceleration of a black hole.
Hawking radiation cannot exist
Through disassembling we can, in principle, retrieve all the information which fell into a black hole, or a frozen star. This is strong evidence against the existence of Hawking radiation. A black hole does not destroy information. The information is, in principle, retrievable. It would be very strange if Hawking radiation could mysteriously destroy this information.
The resolution of the famous black hole information paradox is that Hawking radiation does not exist.
In this blog we have harshly criticized the hypothesis that Hawking radiation exists. Stephen Hawking used a wrong interpretation of creation operators in (scalar) quantum field theory.
Hawking radiation seems to break unitarity, which is very strong evidence against its existence.
Also, it is not clear how Hawking radiation could obey conservation of energy and momentum.
The temperature of a black hole
A frozen star contains a lot of information, or entropy. Should the star radiate infrared because it has this entropy?
Let us consider a block of glass. Since it is amorphous matter, it contains a lot of entropy or information. Let us cool the block of glass very close to absolute zero. Does the block of glass radiate infrared?
The atoms in the glass will extremely slowly arrange themselves into crystals, releasing some heat. This heat will radiate away. But the flux of infrared is extremely slow.
Is there any lower limit how much infrared should some amount of entropy S radiate?
The Bekenstein hypothesis of entropy: the Bekenstein bound
The hypothesis of Jacob Bekenstein claims that a black hole has an entropy which is proportional to the area of the horizon.
The hypothesis is suspicious. If we throw a crystal into a black hole, why should the entropy of the falling crystal grow to match the (large) Bekenstein value for a black hole?
Also, is there any proof that no ordinary object can have an entropy greater than the Bekenstein value?
If we have one kilogram of noninteracting photons in a cubic meter, one can use quantum mechanics to calculate the number of possible microstates. The value probably agrees with the Bekenstein hypothesis.
What happens if we add interactions? Intuitively, the system is now more "complex", and there might be many more microstates available. For example, in a solid, there are sound waves. Jacob Bekenstein in his 1981 paper ignores interactions.
If we add one very low-energy photon into a vessel whose size is a cubic meter, the photon can take only a few different states, because its wavelength is ~ 1 meter.
If we add a phonon of the same energy into a cubic meter of a solid, the wavelength is much less than that of the photon. It has a huge number of different states.
Wikipedia claims that the Bekenstein bound for the entropy of 1 kg in 1 m³ was proved by Horacio Casini in 2008, in quantum field theory:
Since the problem is very general, it is doubtful that one can solve it in quantum field theory alone.
The temperature T of a system with entropy under a low gravity potential: no infrared radiation is necessary
Let us have a block B of matter at some temperature T. It radiates a certain black body infrared spectrum at a power W.
We move the block B onto the surface of a very heavy neutron star. The spectrum of the block B is greatly redshifted, and the radiation power W' is now much less than W.
If we put B into ever lower gravity potential, is there a limit how close to zero can W' be?
Apparently, not.
There is no requirement that a black hole or a frozen star should radiate infrared at all. The local time there runs extremely slowly. Thermodynamics does not say that something like Hawking radiation should necessarily exist.
Conclusions
We sketched a method which can, in principle, be used to disassemble a black hole or a frozen star.
This resolves the famous black hole information paradox: the information is preserved inside the frozen star, and Hawking radiation does not exist.
We will do more research on the Bekenstein bound. Do interactions allow to store much more entropy into a 1 kg mass in a cubic meter?
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