A topological charge of black holes

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.