Firewalls, black-hole thermodynamics, and singular solutions of the Tolman-Oppenheimer-Volkoff equation

TL;DR

This paper models a self-gravitating perfect fluid near a black hole using the TOV equation, revealing a high-temperature firewall with Planck-scale densities surrounding a negative mass singularity, and relates its entropy to Bekenstein-Hawking entropy.

Contribution

It introduces a novel solution to the TOV equation showing a firewall-like structure with Planck-scale properties around a black hole, challenging traditional horizon concepts.

Findings

Firewall with Planck-scale temperature and density

Absence of horizon at Schwarzschild radius

Firewall entropy comparable to Bekenstein-Hawking entropy

Abstract

We investigate thermodynamic equilibrium of a self-gravitating perfect fluid in a spherically symmetric system containing a black hole of mass M by means of the Tolman-Oppenheimer-Volkoff (TOV) equation. At r >> 2M its solutions describe a black-body radiation atmosphere with the Hawking temperature T_BH~1/(8 \pi M) that is increasingly blueshifted as r approaches 2M. However, there is no horizon at the Schwarzschild radius. Instead, the fluid becomes increasingly hot and dense there, piling up into a "firewall" with the peak temperatures and densities reaching Planck values somewhat below r = 2M. This firewall surrounds a negative point mass residing at r=0, the only singularity of the solution. The entropy of the firewall is comparable to the Bekenstein-Hawking entropy.