Why is the black hole entropy (almost) linear in the horizon area?

Details Why is the black hole entropy (almost) linear in the horizon area? Why is the black hole entropy (almost) linear in the horizon area?

2000-11-07

arxiv.org/abs/gr-qc/0011024v2

Phys.Rev. D63 (2001) 064005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages, references added and corrected, approved for publication in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.63.064005

We show that essentially pure classical thermodynamics is sufficient to determine Bekenstein's formula for the black hole's entropy, $S=\eta A$. We base our reasoning on the minimal assumption that since black body radiation is describable by classical thermodynamics, so is the complete black hole-Hawking radiation system. Furthermore, we argue that any non-linear correction to the black hole entropy must be quantum mechanical in nature. The proportionality coefficient, $\eta=1/4\ell_P^2$, must be calculated within a semi-classical or full-fledged quantum mechanical framework.

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