Phys.Rev.D, 110, 024028 (2024)

Notes on sums over horizons

Peng Zhao¹ and Hong Lü^1,2

1 Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Binhai New City, Fuzhou 350207, China.

2 Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University, Tianjin 300350, China.

* mrhonglu@gmail.com

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.