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

Understand

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.