Origin of BH Entropy & Info Missing Puzzle Resolution

[sufive]

TL;DR Summary

A unifying resolution to the problem of black hole entropy's origin and information missing puzzle

Dear everyone, I wish to discuss in this thread a classic/semi-classic interpretation on the origin of Bekenstein-Hawking entropy and the related resolution to Hawking's information missing puzzle, which were published in Nucl.Phys.B977 (2022) 115722 and Nucl.Phys.B990 (2023) 116171 after strictly executed peer review. I myself believe it's the most possible final resolution to these two key questions in theoretical black hole physics. But of course I would like to accept your critics if your critics hit the point indeed.

My interpretation for the origin of BH entropy is based on an exact solutions family to the Einstein equation sourced by a representing dust gas. The outside part of the solution is exactly Schwarzschild type. But its inside part is characterised by an initial radial mass profile M(rho) and a following ``collapsing’’ function a(tau,rho) which I called Over Cross Oscillation. Schematically, the solutions family can be written as,

ds^2=-dtau^2+F(tau,M[rho])drho^2+a[…]^2rho^2dOmega^2 ……(1)

OCO means that, when two dust particles hit on the central point, the east semi-sphere incomer over crosses to the west semi-sphere and vice versa. Both of them do not stay there or become a part of the previously formed singularity. This solution does not break the singularity theorem but resolves the conventionally understood singularity from a once and for all (eternal) one into a periodically forming and resolving one.

Through a canonic quantisation of the Einstein equation under the metric ansatz (1), I got a wave functional description of the dust ball, which I called as OCO fuzzball due to its horizon’s being blurred by the quantum fluctuation. At the same time, I found that after the quantisation, both the classically arbitrary initial mass profile M[rho] and the oscillation modes a[tau] becomes discrete and countable, with the degeneracy exactly consistent with the area law formula of BH entropy. This way, I claim that I got a classic or semi-classic interpretation for the origin of BH entropy.

With my interpretation for the BH entropy, the black hole becomes a completely normal object, just like the usual atom with inner structures. This allows me to study its gravity induced spontaneous radiation (which I shortened as GISR) through an explicitly hermitian hamiltonian,

H=H_bh+H_vac+H_int ……(2)

the first part is chosen as a diagonal matrix which represents all microscopic states of the black hole with various masses. The second part describes the vacuum fluctuation around the black hole which is represented by many harmonic oscillators. The third part couples the vacuum fluctuation modes and microscopic states of the black hole so that, every time a vacuum mode gets on shell, the black hole transitions between two special modes at a corresponding probability amplitude.

I proved that due to the exponential degeneracy of the black hole's microscopic state, the spectrum of GISR(2) is exactly of the thermal type and has exactly the same temperature as hawking radiation. For this reason, I argue that GISR is the underlying mechanism of hawking radiation. But because it is described by an explicitly hermitian hamiltonian, it involves no information missing and has the desired feature of Page curve when I compute the entropy of the black hole or the radiation particles.

Although GISR involves information missing, it makes the cause of information missing in Hawking’s argument transparent. The cause has two aspects: (i) exact thermal spectrum is only an instantaneous feature of GISR. A full evaporation evolution of a black hole is a non-equilibrium process and is characterised by a time dependent temperature curve. For different microscopic initial black hole, this curve is different. Hawking’s calculation gives up this feature completely. (ii) Hawking’s argument takes the evaporating black hole as a classic object with time dependent mass and neglects the entanglement superposition of different mass black holes and the corresponding radiation particles. That is, the proper middle state of the system should be written as

Psi[BH(t)]= BH_0*HwkPtcl_none+BH_big*HwkPtcl_little+BH_mid*HwkPtcl_some+... (3)

The superposition (3) looks very much like the state of dead+living cat in Schrodinger’s gedanken experiment. It is a must be in a full quantum treatment of a black hole’s radiation evolution. But in Hawking’s argument for information missing puzzle, it is neglected and the middle state of the black hole is written as
Psi[BH(t)]=BH_mass(t) (4)

 

[PeterDonis]

which were published in Nucl.Phys.B977 (2022) 115722 and Nucl.Phys.B990 (2023) 116171

Please give links to the actual publication pages.

 

[sufive]

The actual publication pages is as follows:
https://www.sciencedirect.com/science/article/pii/S0550321323001001?via=ihub
https://www.sciencedirect.com/science/article/pii/S0550321322000736?via=ihub
Another point which I wish to add here is, it's more appropriate to say "I myself believe it's the solution most closely related to the underlying physics reality" than ``the most possible final resolution to these two key questions''

 

[Demystifier]

I have looked at the paper you attached and it looks nonsensical to me at several levels. Let me just focus on one thing. In Eq. (16) you describe evolution as a series of Penrose diagrams. But each Penrose diagram is a spacetime diagram, meaning that each Penrose diagram describes an evolution by itself. So how can evolution be described by a series of Penrose diagrams?

 

[sufive]

I notified in the paper after eq(17) that `` where PC-diagram with different length of zigzag part denotes different size black holes and their corresponding radiation products''. So the Penrose diagram in eq(16) is not the usual diagram you understood denoting an evolving space-time.

 

[Demystifier]

In the Appendix you seem to say that horizon is not needed for Hawking radiation. I would recommend you to read https://arxiv.org/abs/hep-th/0106111 which points out that event horizon is not needed, but apparent horizon is needed. Neutron star, in particular, does not have an apparent horizon and hence cannot produce Hawking radiation.

 

[sufive]

Thank you very much for the recommendation of papers, I will read it. On the question of hawking radiation needs/not horizon, my viewpoint is that: hawking radiation is a result but not a mechanism. This result says that the fixed position observers can measure particles from the vacuum defined by the freely falling observers. But its underlying mechanism is unknown. If the gravity induced spontaneous radiation is the underlying mechanism as I argue, then the horizon is not need for it.