The Membrane Paradigm and Firewalls

Following the Membrane Paradigm, we show that the stretched horizon of a black hole retains information about particles thrown into the hole for a time of order the scrambling time m ln(m/M_P), after the particles cross the horizon. One can, for example, read off the proper time at which a particle anti-particle pair thrown into the hole, annihilates behind the horizon, if this time is less than the scrambling time. If we believe that the Schwarzschild geometry exterior to the horizon is a robust thermodynamic feature of the quantum black hole, independent of whether it is newly formed, or has undergone a long period of Hawking decay, then this classical computation shows that the "firewall" resolution of the AMPS paradox is not valid.

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