Mass of a Black Hole Firewall

Understand

Quantum entanglement of Hawking radiation has been supposed to give rise to a Planck density "firewall" near the event horizon of old black holes.

• We show that Planck density firewalls are excluded by Einstein's equations for black holes of mass exceeding the Planck mass.
• We find an upper limit of $1/(8\pi M)$ to the surface density of a firewall in a Schwarzschild black hole of mass $M$, translating for astrophysical black holes into a firewall density smaller than Planck density by more than 30 orders of magnitude.
• A strict upper limit on the firewall density is given by the Planck density times the ratio $M_{\rm Pl}/(8\pi M)$.