Notes on sums over horizons

TL;DR

This paper demonstrates that for many black holes, the sum of thermodynamic quantities across all horizons is dictated by data at infinity, introduces a new computation method, and discusses higher-curvature effects.

Contribution

It provides a general proof linking horizon sums to asymptotic data and proposes a novel approach to compute entropy sums, extending to higher-curvature gravity.

Findings

Sum of thermodynamic quantities determined by asymptotic data

New method for entropy sum calculation using generalized Smarr formula

Higher-curvature corrections in Gauss-Bonnet gravity analyzed

Abstract

For a large class of black holes, we show that the sum of thermodynamic quantities over all the horizons is determined by the asymptotic data at infinity. For the Kerr-Newman metric, this proves a recent numerical observation by Hristov. We propose a new method to compute the sum of the entropies using a generalized Smarr formula. The higher-curvature corrections in Gauss-Bonnet gravity are discussed.