Rindler Energy is Wald Entropy

Abstract

We show that, in any theory of gravity, the entropy of any nonextreme black hole is given by $2 \pi E_R$ where $E_R$ is the dimensionless Rindler energy. Separately, we show that $E_R$ is exactly Wald's Noether charge and therefore this entropy is identical to Wald entropy. However, it is off--shell and derived solely from the time evolution of the black hole. We examine Gauss--Bonnet black holes as an example and speculate on the degrees of freedom that $E_R$ counts.