Nonextremal black holes in gauged supergravity and the real formulation of special geometry

TL;DR

This work develops a general recipe to construct nonextremal black holes in ${\cal N}=2$, ${\rm D}=4$ Fayet-Iliopoulos gauged supergravity by applying time-like dimensional reduction and the real formulation of special geometry, enabling solution generation beyond BPS cases. It produces explicit nonextremal, static solutions for several simple prepotentials (notably $F = -i X^0 X^1$ and $F = -2i\sqrt{X^0 (X^1)^3}$) in axion-free sectors, organized as three-parameter families governed by harmonic data and a quartic warp factor $e^{2\psi}$. The paper also analyzes thermodynamics (temperature and entropy) and shows how BPS limits emerge from charge relations, while discussing the limitations and potential extensions (e.g., for the $F = -(X^1)^3/X^0$ model) and positing questions about horizon-structure universality. Overall, the results extend nonextremal black hole constructions in gauged ${\cal N}=2$ supergravity and provide a framework for exploring broader prepotentials and first-order reformulations.

Abstract

We give a rather general recipe for constructing nonextremal black hole solutions to N=2, D=4 gauged supergravity coupled to abelian vector multiplets. This problem simplifies considerably if one uses the formalism developed in arXiv:1112.2876, based on dimensional reduction and the real formulation of special geometry. We use this to find new nonextremal black holes for several choices of the prepotential, that generalize the BPS solutions found in arXiv:0911.4926. Some physical properties of these black holes are also discussed.