Pure states and black hole complementarity

TL;DR

This paper demonstrates that for generic pure states, black hole complementarity holds after the Page time, as deviations from thermality are negligible, ensuring infalling observers experience no drama at the horizon.

Contribution

It provides a derivation of black hole complementarity for generic pure states, showing minimal deviations from thermality near the horizon after the Page time.

Findings

Infalling observers see no drama at the horizon for generic pure states.

Deviations from thermality are exponentially small for typical states.

Atypical states may exhibit surprises, but are not representative of generic behavior.

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.