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

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 πM) 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.

We study self-gravitating spherically symmetric fluid with a mass of a black hole surrounded by Hawking radiation. Solutions cross r=2M without encountering coordinate singularity to reach a firewall-like "Planck cocoon" with entropy close to black hole entropy. We reproduce our paper with an updated title and abstract. For a later study with similar results see G. 't Hooft, gr-qc/9706058