Flow Equations for Non-BPS Extremal Black Holes

TL;DR

This paper develops a method to describe stable non-BPS extremal black holes using first-order equations driven by a superpotential, expanding understanding beyond BPS solutions in supergravity theories.

Contribution

It introduces a general procedure to construct non-BPS extremal black holes with a superpotential, replacing the central charge in the black hole potential.

Findings

Constructed a class of stable non-BPS extremal black holes

Provided a method to derive the superpotential for these solutions

Identified cases with similar behavior outside the main class

Abstract

We exploit some common features of black hole and domain wall solutions of (super)gravity theories coupled to scalar fields and construct a class of stable extremal black holes that are non-BPS, but still can be described by first-order differential equations. These are driven by a "superpotential'', which replaces the central charge Z in the usual black hole potential. We provide a general procedure for finding this class and deriving the associated "superpotential''. We also identify some other cases which do not belong to this class, but show a similar behaviour.