The Sensitivity of Black Holes to Low Energy Excitations

TL;DR

This paper investigates how low energy excitations affect observables near black hole horizons in AdS space, showing that certain apparent violations of statistical mechanics bounds are resolved under specific conditions.

Contribution

It demonstrates that restrictions on excitations and observables eliminate apparent violations of statistical bounds near black hole horizons in AdS/CFT.

Findings

Violations of statistical mechanics bounds near black holes can be avoided with boundary source restrictions.

Single causal patch observables do not exhibit violations under these restrictions.

The results clarify the conditions under which black hole interior descriptions are consistent with statistical mechanics.

Abstract

A general principle of statistical mechanics is that low energy excitations of a thermal state change expectation values of observables by a very small amount. However some observables in the vicinity of the horizon of a large black hole in anti-de Sitter space naively seem to violate this bound. This potential violation is related to the question of whether the black hole interior can be described in AdS/CFT. Here we point out that if the possible excitations are limited to those produced by a simple local source on the boundary, and the possible observables are limited to products of field operators in a single causal patch in the bulk, then these violations disappear.