Mass formulae for a class of nonrotating black holes

TL;DR

This paper derives quadratic relations, called mass formulae, linking the asymptotic fluxes to horizon properties for certain nonrotating black holes with scalar and vector fields, using sigma-model structures.

Contribution

It introduces a new method to derive mass formulae for nonrotating black holes in Einstein-matter theories with scalar and vector fields, including string theory models.

Findings

Quadratic relations between flux integrals and horizon parameters.

Application to Einstein-Maxwell and Einstein-Maxwell-axion-dilaton models.

Relevance to heterotic string theory black holes.

Abstract

In the presence of a Killing symmetry, various self-gravitating field theories with massless scalars (moduli) and vector fields reduce to sigma-models, effectively coupled to 3-dimensional gravity. We argue that this particular structure of the Einstein-matter equations gives rise to quadratic relations between the asymptotic flux integrals and the area and surface gravity (Hawking temperature) of the horizon. The method is first illustrated for the Einstein-Maxwell system. A derivation of the quadratic formula is then also presented for the Einstein-Maxwell-axion-dilaton model, which is relevant to the bosonic sector of heterotic string theory.