Thermal corpuscular black holes

TL;DR

This paper models evaporating black holes as quantum states of many bosons, deriving entropy and Hawking radiation properties, and showing evaporation halts at zero mass in this quantum framework.

Contribution

It introduces a quantum corpuscular model of black holes with a specific state structure, deriving entropy and radiation corrections, and analyzing backreaction effects.

Findings

Entropy follows the area law with a logarithmic correction.

Hawking flux is reduced by backreaction effects.

Black hole evaporation stops at zero mass in this model.

Abstract

We study the corpuscular model of an evaporating black hole consisting of a specific quantum state for a large number $N$ of self-confined bosons. The single-particle spectrum contains a discrete ground state of energy $m$ (corresponding to toy gravitons forming the black hole), and a gapless continuous spectrum (to accommodate for the Hawking radiation with energy $\omega>m$). Each constituent is in a superposition of the ground state and a Planckian distribution at the expected Hawking temperature in the continuum. We first find that, assuming the Hawking radiation is the leading effect of the internal scatterings, the corresponding $N$-particle state can be collectively described by a single-particle wave-function given by a superposition of a total ground state with energy $M=N\,m$ and a Planckian distribution for $E>M$ at the same Hawking temperature. From this collective state, we compute the partition function and obtain an entropy which reproduces the usual area law with a logarithmic correction precisely related with the Hawking component. By means of the horizon wave-function for the system, we finally show the backreaction of modes with $\omega>m$ reduces the Hawking flux. Both corrections, to the entropy and to the Hawking flux, suggest the evaporation properly stops for vanishing mass, if the black hole is in this particular quantum state.