Pure states and black hole complementarity

Understand

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.