Complementarity is not enough

Abstract

The near-horizon field $B$ of an old black hole is maximally entangled with the early Hawking radiation $R$, by unitarity of the S-matrix. But $B$ must be maximally entangled with the black hole interior $A$, by the equivalence principle. Causal patch complementarity fails to reconcile these conflicting requirements. The system $B$ can be probed by a freely falling observer while there is still time to turn around and remain outside the black hole. Therefore, the entangled state of the $BR$ system is dictated by unitarity even in the infalling patch. If, by monogamy of entanglement, $B$ is not entangled with $A$, the horizon is replaced by a singularity or ``firewall.'' To illustrate the radical nature of the ideas that are needed, I briefly discuss two approaches for avoiding a firewall: the identification of $A$ with a subsystem of $R$; and a combination of patch complementarity with the Horowitz-Maldacena final-state proposal.