Pure states and black hole complementarity

Abstract

The future apparent horizon of a black hole develops large stress energy due to quantum effects, unless the outgoing modes are in a thermal density matrix at the local Hawking temperature. It is shown for generic pure states that the deviation from thermality is so small that an infalling observer will see no drama on their way to the stretched horizon, providing a derivation of black hole complementarity after the Page time. Atypical pure states, and atypical observers, may of course see surprises, but that is not surprising.