Black hole entropy from the quantum atmosphere of bound gravitational fluctuations

TL;DR

This paper proposes that black hole entropy can be understood through the quantum atmosphere of gravitational fluctuations near the horizon, linking trapped modes to the spacetime's dynamical degrees of freedom and observable effects.

Contribution

It introduces a novel approach to black hole entropy based on the density of states of trapped gravitational modes sourced by Hawking-Unruh radiation, incorporating a Planck-scale cutoff.

Findings

Density of states derived from Regge-Wheeler-Zerilli equation

Entropy cutoff by Planck scale near the horizon

Characteristic frequencies around 100 Hz for solar mass black holes

Abstract

Black hole entropy is identified with the counting of the dynamical degrees of freedom of trapped gravitational modes continually sourced by the Hawking-Unruh process. In the context of linear perturbations of Schwarzschild spacetime the density of states is derived from the orthogonality of states in the solution space of the Regge-Wheeler-Zerilli equation. The otherwise divergent energy and entropy is cutoff by the Planck scale closest approach of constantly accelerating observers near the horizon. The thermal distribution of the trapped modes, which represent shape fluctuations in the near horizon geometry, store a significant fraction of the spacetime mass as observed from far away. Unlike quasi-normal modes the modes are not directly observable outside of $\sim 3 M$ but, being external to the horizon, they affect the propagation of null rays near the black hole. The characteristic frequencies, around 100 Hz for solar mass black holes, are discussed in relation to possible observations.