A topological charge of black holes

TL;DR

This paper introduces a topological charge for black holes, showing it completes the thermodynamic description in various gravity theories and aligns with holographic principles.

Contribution

It identifies and incorporates a previously overlooked topological charge into black hole thermodynamics across multiple gravity frameworks.

Findings

Topological charge completes the black hole thermodynamic relations.

The charge fits within holographic and Lovelock-Maxwell theories.

It extends the understanding of black hole charges beyond known parameters.

Abstract

The topological charge of a maximally symmetric black hole naturally arises in holography, which can be viewed as the last charge of the black hole in the sense that it together with all other known charges satisfies the holographic Gibbs-Duhem-like relation as a completeness relation. It is then observed that this topological charge, which we have missed before, fits perfectly into the black hole thermodynamics from two different approaches, not only in Einstein's gravity, but also in the general Lovelock-Maxwell theory.