Post-firewall paradoxes
We derive two variations of the firewall paradox for evaporating black holes. Our approach sweeps away many unnecessary assumptions. There is no need: to assume ‘nice slices’ through the black hole spacetime; to decode Hawking radiation; to make any assumptions about the physics of Planck scale black holes; and other simplifications. Theorem 1: A contradiction exists between: 1.a) completely unitarily evaporating black holes, 1.b) a freely falling observer notices nothing special until they pass well within a large black hole’s horizon, and 1.c) the black hole interior Hilbert space dimensionality may be well approximated as the exponential of the Bekenstein-Hawking entropy. Theorem 2: A contradiction exists between: 2.a) completely unitarily evaporating black holes, 2.b) large black holes are described by local physics, and 2.c) externally, a large black hole should resemble its classical theoretical counterpart (aside from its slow evaporation). At least one of these conventionally accepted verities from each theorem must be false.