How fast can a black hole release its information?

TL;DR

Hawking's semiclassical picture implies information loss as black holes radiate away mass. The author argues that string theory's fuzzball microstates provide a vast nonperturbative phase space, allowing a collapsing shell to spread into a superposition of microstates with a tunneling amplitude that is exponentially suppressed per state but vastly compensated by the number of states ${\cal N} \sim e^{GM^2}$. A rough estimate shows the dephasing time for this spreading, t_{tunneling}, is shorter than the Hawking evaporation time t_{evap}, thus information can emerge via fuzzball radiation. This supports a resolution to the information paradox through horizonless microstates and nonperturbative string effects, linking entropy, tunneling, and dynamics in black hole physics.

Abstract

When a shell collapses through its horizon, semiclassical physics suggests that information cannot escape from this horizon. One might hope that nonperturbative quantum gravity effects will change this situation and avoid the `information paradox'. We note that string theory has provided a set of states over which the wavefunction of the shell can spread, and that the number of these states is large enough that such a spreading would significantly modify the classically expected evolution. In this article we perform a simple estimate of the spreading time, showing that it is much shorter than the Hawking evaporation time for the hole. Thus information can emerge from the hole through the relaxation of the shell state into a linear combination of fuzzballs.