On anharmonic stabilisation equations for black holes

TL;DR

This paper explores the stabilization equations for various black holes in four-dimensional N=2 supergravity, revealing that these equations inherently include anharmonic components, even under symmetric and static conditions.

Contribution

It demonstrates that stabilization equations for extremal and non-extremal black holes necessarily contain anharmonic terms, expanding understanding of black hole solutions in supergravity.

Findings

Stabilization equations include anharmonic parts.

An explicit calculation confirms anharmonicity in static, spherically symmetric cases.

Results apply to both supersymmetric and non-supersymmetric black holes.

Abstract

We investigate the stabilisation equations for sufficiently general, yet regular, extremal (supersymmetric and non-supersymmetric) and non-extremal black holes in four-dimensional N=2 supergravity using both the H-FGK approach and a generalisation of Denef's formalism. By an explicit calculation we demonstrate that the equations necessarily contain an anharmonic part, even in the static, spherically symmetric and asymptotically flat case.