The universal property of the entropy sum of black holes in all dimensions

Yi-Qiang Du,Yu Tian

doi:10.1016/j.physletb.2014.10.052

Abstract

It is proposed by Cvetic et al. [1] that the product of all horizon areas for general rotating multi-change black holes has universal expressions independent of the mass. When we consider the product of all horizon entropies, however, the mass will be present in some cases, while another new universal property [2] is preserved, which is more general and says that the sum of all horizon entropies depends only on the coupling constants of the theory and the topology of the black hole. The property has been studied in limited dimensions and the generalization in arbitrary dimensions is not straight-forward. In this Letter, we prove a useful formula, which makes it possible to investigate this conjectured universality in arbitrary dimensions for the maximally symmetric black holes in general Lovelock gravity and f(R) gravity. We also propose an approach to compute the entropy sum of general Kerr–(anti-)de-Sitter black holes in arbitrary dimensions. In all these cases, we prove that the entropy sum depends only on the coupling constants and the topology of the black hole.

Highlights

Studying the black hole entropy has been an attracting work after the establishment of black hole thermodynamics, but it is still a challenge to explain the black hole entropy at the microscopic level
We prove that the entropy sum depends only on the coupling constants of the theory and the topology of the black holes
In order to investigate the property of entropy sum in all dimensions, we find that the formula (9) is very useful for the calculation

Summary

Introduction

Studying the black hole entropy has been an attracting work after the establishment of black hole thermodynamics, but it is still a challenge to explain the black hole entropy at the microscopic level. [11] has studied the entropy product by introducing a number of possible higher curvature corrections to the gravitational action, showing that the universality of this property fails in general It is found by Meng et al [2] that the sum of all horizon entropies including “virtual” horizons has a universal property that it depends on the coupling constants of the theory and the topology of the black hole, but does not depend on the mass and the conserved charges such as the angular momenta Ji and charges Qi. The conjectural property has only been discussed in limited dimensions. It seems that the sum of all entropies including non-physical entropies proposed by [2] has a better performance, which depends only on the coupling constants of the theory and the topology of the black holes. Gauss-Bonnet case, which is included in the Lovelock gravity, obeys the property in all dimensions, and we will give the proof later

A useful formula

Black holes in the Lovelock gravity

Conclusion and discussion