Black Hole Entropy and the Pseudo Goldstone Bosons of Conformal Symmetry

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.