Quantum spectrum and statistic entropy of black hole

TL;DR

This paper models the black hole horizon as a membrane, derives its oscillation modes, and shows that the resulting quantum statistic entropy aligns with the Bekenstein-Hawking entropy, confirming the area law.

Contribution

It introduces a membrane oscillation model for black hole horizons and links the derived quantum entropy to the horizon area, supporting the area law of black hole entropy.

Findings

Oscillation frequencies are proportional to black hole temperature.

Frequencies are not equidistant.

Quantum statistic entropy is proportional to horizon area.

Abstract

Taking the horizon surface of the black hole as a compact membrane and solving the oscillation equation of this membrane by Klein-Gordon equation, we derive the frequencies of oscillation modes of the horizon surface, which are proportional to the radiation temperature of the black hole. However, the frequencies of oscillation modes are not equidistant. Using the distribution of obtained frequencies of oscillation mode we compute the statistic entropy of the black hole and obtain that the statistic entropy of the black hole is proportional to the area of the horizon. Therefore, it is proven that the quantum statistic entropy of the black hole is consistent with Bekenstein-Hawking entropy.