H-FGK formalism for black-hole solutions of N=2, d=4 and d=5 supergravity

TL;DR

This paper introduces a new formalism for analyzing black-hole solutions in N=2 supergravity theories in four and five dimensions, simplifying the equations of motion by using real variables that transform with charges under duality.

Contribution

The authors develop the H-FGK formalism, rewriting the FGK effective action with real variables, making the solution form universal for all spherically symmetric black holes in these models.

Findings

Simplified equations of motion for black holes in N=2 supergravity.

Unified solution form for all spherically symmetric black holes.

Applicable to both supersymmetric and non-supersymmetric cases.

Abstract

We rewrite the Ferrara-Gibbons-Kallosh (FGK) black-hole effective action of N=2, d=4,5 supergravities coupled to vector multiplets, replacing the metric warp factor and the physical scalars with real variables that transform in the same way as the charges under duality transformations, which simplifies the equations of motion. For a given model, the form of the solution in these variables is the same for all spherically symmetric black holes, regardless of supersymmetry or extremality.