Remarks on the black hole information problem

String theory provides numerous examples of duality between gravitational theories and unitary gauge theories. To resolve the black hole information paradox in this setting, it is necessary to better understand how unitarity is implemented on the gravity side. We argue that unitarity is restored by nonlocal effects whose initial magnitude is suppressed by the exponential of the Bekenstein-Hawking entropy. Time-slicings for which effective field theory is valid are obtained by demanding the mutual back-reaction of quanta be small. The resulting bounds imply that nonlocal effects do not lead to observable violations of causality or conflict with the equivalence principle for infalling observers, yet implement information retrieval for observers who stay outside the black hole.

Figure 1

Timeslices can be constructed in the semiclassical geometry that simultaneously intersect most of the Hawking radiation and a freely falling observer who crosses the horizon early on.

Figure 2

A set of timeslices satisfying the back-reaction bound, and for which an observer hovering close to the horizon remains at low energy.

Figure 3

Signal propagation from ${\mathcal{O}}_{\mathrm{free}}$ to ${\mathcal{O}}_{\mathrm{accel}}$ is restricted by the black hole geometry.