Factorization of unitarity and black hole firewallsFrom the paper:
Stephen D.H. Hsu
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.
... An objection to the importance of macroscopic superpositions to the information problem is that there is much less information in the coarse grained position or even trajectory (sequence of positions) of the black hole than in the radiation. From this perspective one should be able to neglect the superposition of spacetimes and demand approximate unitarity branch by branch -- in other words, impose factorization. Below, we show that the firewall argument depends sensitively on the precision of factorization. Once macroscopic superpositions are taken into account, the required deviation of near-horizon modes from the inertial vacuum state becomes extremely small. ...
The quantum evolution of a complex pure state typically leads to a superposition of decoherent semiclassical states. In the case of black hole evaporation one obtains a superposition of spacetime geometries because the Hawking radiation inevitably exhibits fluctuations in energy and momentum density over different regions. Firewall and information paradoxes result from the non-trivial assumption of factorization: approximate unitarity on each decoherent geometry. Global unitarity is a much weaker condition than factorization. Quantum correlations between geometries can plausibly resolve the information paradoxes, although specific dynamical mechanisms are still not understood.