Factorization of unitarity and black hole firewalls

Unitary black hole evaporation necessarily involves a late-time superposition of decoherent states, including states describing distinct spacetimes (e.g., different center of mass trajectories of the black hole). Typical analyses of the black hole information problem, including the argument for the existence of firewalls, assume approximate unitarity ("factorization of unitarity") on each of the decoherent spacetimes. This factorization assumption is non-trivial, and indeed may be incorrect. We describe an ansatz for the radiation state that violates factorization and which allows unitarity and the equivalence principle to coexist (no firewall). Unitarity without factorization provides a natural realization of the idea of black hole complementarity.