First-order flows and stabilisation equations for non-BPS extremal black holes

TL;DR

This paper derives generalized flow equations for non-BPS extremal black holes in four-dimensional supergravity, providing stabilisation equations for scalars and a new ansatz involving harmonic functions.

Contribution

It introduces a unified framework for non-BPS black hole solutions, extending known BPS stabilisation equations and proposing a novel ansatz with harmonic function ratios.

Findings

Derived generalized flow equations for non-BPS black holes

Provided stabilisation equations for specific charge vectors

Proposed a new ansatz involving ratios of harmonic functions

Abstract

We derive a generalised form of flow equations for extremal static and rotating non-BPS black holes in four-dimensional ungauged N = 2 supergravity coupled to vector multiplets. For particular charge vectors, we give stabilisation equations for the scalars, analogous to the BPS case, describing full known solutions. Based on this, we propose a generic ansatz for the stabilisation equations, which surprisingly includes ratios of harmonic functions.