Black Hole Entropy and the Pseudo Goldstone Bosons of Conformal Symmetry

TL;DR

This paper explores how the conformal symmetry near nonextremal black hole horizons, broken by the Rindler vacuum, can be described by pseudo Goldstone bosons and their Schwarzian action, linking to black hole entropy.

Contribution

It introduces a framework connecting conformal symmetry breaking near black holes to pseudo Goldstone bosons and derives the Schwarzian action related to black hole entropy.

Findings

Schwarzian action reproduces Wald entropy for nonextremal black holes

Conformal symmetry breaking is linked to pseudo Goldstone bosons

Results align with near extremal charged black holes in near AdS2 spaces

Abstract

The very near horizon regions of nonextremal black holes have a conformal symmetry which is anomalous and spontaneously broken by the Rindler vacuum. Therefore, these black holes can effectively be described by the pseudo Goldstone bosons of conformal symmetry and their Schwarzian action which is determined by the breakdown of the conformal symmetry to $SL(2)$. In Euclidean gravity, the Schwarzian action leads to the Wald entropy of nonextremal black holes. These results are consistent with the neutral limit of near extremal charged black holes described by near $AdS_2$ space--times.