The information paradox and the infall problem

TL;DR

The paper demonstrates through a simple model that small quantum gravity corrections cannot resolve the black hole information paradox, emphasizing the need for order unity modifications at the horizon, and distinguishes between the information paradox and the infall problem.

Contribution

It provides an explicit model illustrating the entanglement inequality and separates the black hole puzzles into two distinct issues: the information paradox and the infall problem.

Findings

Small corrections do not significantly reduce entanglement entropy.

Order unity corrections are necessary to resolve the information paradox.

The black hole puzzles are split into the information paradox and the infall problem.

Abstract

It is sometimes believed that small quantum gravity corrections to the Hawking radiation process can encode the correlations required to solve the black hole information paradox. Recently an inequality on the entanglement entropy of radiation was derived, which showed that such is not the case; one needs {\it order unity} corrections to low energy modes at the horizon to resolve the problem. In this paper we illustrate this inequality by a simple model where the state of the created Hawking pair at each stage is slightly modified by the state of the previous pair. The model can be mapped onto the 1-dimensional Ising chain and solved explicitly. In agreement with the general inequality we find that very little of the entanglement is removed by the encoded correlations. We then use the general inequality to argue that the black hole puzzles split into two problems: the `information paradox' and the `infall problem'. The former addresses the detailed state of low energy modes at the horizon and asks if these can be modified by order unity, while the latter asks for a coarse grained effective description of the infall of heavy observers into the degrees of freedom of the hole.