Extremality Versus Supersymmetry in Stringy Black Holes

TL;DR

This paper investigates black hole solutions in string theory, analyzing extremality conditions, charge relations, and the distinction between supersymmetric and non-supersymmetric extremal black holes across various dimensions.

Contribution

It provides a unified metric framework for black holes in string theory, characterizes extremality conditions, and explores the prevalence of non-supersymmetric extremal black holes suggesting higher-dimensional structures.

Findings

Temperature vanishes at extremality.

Number of charge combinations leading to extremality is 2^{(n-1)}.

Existence of non-supersymmetric extremal black holes implies potential twelve-dimensional structure.

Abstract

We study general black-hole solutions of the low-energy string effective action in arbitrary dimensions using a general metric that can describe them all in a unified way both in the extreme and non-extreme cases. We calculate the mass, temperature and entropy and study which relations amongst the charges and the mass lead to extremality. We find that the temperature always vanishes in the extreme limit and we find that, for a set of n charges (no further reducible by duality) there are 2^{(n-1)} combinations of the charges that imply extremality. Not all of these combinations can be central charge eigenvalues and, thus, there are in general extreme black holes which are not supersymmetric (or ``BPS-saturated''). In the N=8 supergravity case we argue that the existence of roughly as many supersymmetric and non-supersymmetric extreme black holes suggests the existence of an underlying twelve-dimensional structure.