Quasi-normal modes and Microscopic Structure of the Schwarzschild Black Hole

TL;DR

This paper models Schwarzschild black holes as a collection of quantum harmonic oscillators, deriving entropy corrections and holographic scaling consistent with known quantum gravity results.

Contribution

It introduces a novel statistical ensemble approach to black hole microstructure using quantum harmonic oscillators, reproducing entropy and holographic properties.

Findings

Gibbs entropy matches Bekenstein-Hawking entropy in large-mass limit

Logarithmic entropy correction consistent with literature

Oscillator number scales holographically with horizon area

Abstract

Maggiore observed that, in the high-damping regime, the quasi-normal modes spectrum for the Schwarzschild black hole resembles that of a quantum harmonic oscillator. Motivated by this observation, we describe a black hole as a statistical ensemble of N quantum harmonic oscillators. By working in the canonical ensemble, we show that, in the large-mass black hole limit, the leading contribution to the Gibbs entropy is the Bekenstein-Hawking term, while the subleading one is a logarithmic correction, in agreement with several results in the literature. We also find that the number of oscillators scales holographically with the area of the event horizon.