Comment on "The black hole final state"

Abstract

Horowitz and Maldacena have suggested that the unitarity of the black hole S-matrix can be reconciled with Hawking's semiclassical arguments if a final-state boundary condition is imposed at the spacelike singularity inside the black hole. We point out that, in this scenario, departures from unitarity can arise due to interactions between the collapsing body and the infalling Hawking radiation inside the event horizon. The amount of information lost when a black hole evaporates depends on the extent to which these interactions are entangling.

Figures (1)

• Figure 1: Information flow in the evaporating black hole, according to the Horowitz-Maldacena (HM) proposal. Here time runs from right to left, $|n\rangle_{M}$ is the initial quantum state of the collapsing body, and $|m\rangle_{out}$ is the final quantum state of the outgoing Hawking radiation emitted during evaporation. The ket $|\Phi\rangle_{in\otimes out}$ is the maximally-entangled Unruh state of the infalling and outgoing Hawking radiation, and the bra ${}_{M\otimes in}\langle \Phi|$ is the (maximally-entangled) boundary condition imposed at the spacelike singularity. $S$ is the unitary black-hole $S$-matrix, which HM absorb into the boundary condition. The unitary matrix $U$, not considered by HM, arises from interactions between the collapsing body and the infalling radiation inside the event horizon.