First-order flow equations for extremal black holes in very special geometry

TL;DR

This paper develops first-order flow equations for extremal black holes in N=2 supergravity, providing new solutions for non-supersymmetric cases by connecting five- and four-dimensional geometries.

Contribution

It introduces a novel method to derive and solve flow equations for extremal black holes in four-dimensional supergravity using five-dimensional Taub-NUT geometries.

Findings

Derived first-order flow equations for extremal black holes.

Constructed explicit solutions for non-supersymmetric black holes.

Established a connection between 5D and 4D black hole solutions.

Abstract

We construct interpolating solutions describing single-center static extremal non-supersymmetric black holes in four-dimensional N=2 supergravity theories with cubic prepotentials. To this end, we derive and solve first-order flow equations for rotating electrically charged extremal black holes in a Taub-NUT geometry in five dimensions. We then use the connection between five- and four-dimensional extremal black holes to obtain four-dimensional flow equations and we give the corresponding solutions.