Tunneling into fuzzball states
Samir D. Mathur
TL;DR
Problem: the information paradox arises when a collapsing shell forms a horizon and Hawking radiation would erase information. Method: the paper proposes that the shell tunnels into the large ensemble of horizonless fuzzball microstates, with tunneling amplitude $A \sim e^{-S_{tunnel}}$ and state count $\mathcal{N} \sim e^{S_{bek}}$, enabling a transition on a timescale $t_{stabilization} \lesssim t_{evap}$. Findings: $S_{tunnel} \sim \alpha GM^2$ and $S_{bek} \sim GM^2$, so the small amplitude can be offset by the enormous state count, allowing information-rich fuzzball radiation before significant Hawking loss. Significance: provides a mechanism to preserve unitarity in black hole formation and evaporation within the fuzzball framework by tying the entropy to the feasibility of quantum transitions between macroscopic configurations.
Abstract
String theory suggests that black hole microstates are quantum, horizon sized `fuzzballs', rather than smooth geometries with horizon. Radiation from fuzzballs can carry information and does not lead to information loss. But if we let a shell of matter collapse then it creates a horizon, and it seems that subsequent radiation will lead to information loss. We argue that the resolution to this problem is that the shell can tunnel to the fuzzball configurations. The amplitude for tunneling is small because we are relating two macroscopically different configurations, but the number of states that we can tunnel to, given through the Bekenstein entropy, is very large. These small and large numbers can cancel each other, making it possible for the shell to tunnel into fuzzball states before a significant amount of radiation has been emitted. This offers a way to resolve the information paradox.