Complementarity Is Not Enough

TL;DR

This paper discusses the conflicting entanglement requirements of black hole horizons and interiors, arguing that complementarity fails and suggesting radical new ideas to resolve the firewall paradox.

Contribution

It highlights the limitations of causal patch complementarity and explores novel approaches to resolve the black hole firewall paradox.

Findings

Entanglement of B with R is dictated by unitarity.

Entanglement of B with A leads to firewall or singularity.

Proposes alternative approaches to avoid firewall.

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.