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

TL;DR

This paper develops a method to find nonextremal black hole solutions in gauged supergravity, extending previous work to more complex models and providing a general recipe for non-BPS extremal solutions, with detailed analysis of their properties.

Contribution

It introduces a new systematic approach to construct nonextremal and non-BPS extremal black holes in N=2 gauged supergravity, generalizing previous solutions and linking them via a charge rotation matrix.

Findings

Constructed new nonextremal black hole solutions for complex models.

Derived a general recipe for non-BPS extremal solutions under axion-free conditions.

Analyzed the mass and horizon area relations for these black holes.

Abstract

In arXiv:1207.2679 a new prescription for finding nonextremal black hole solutions to N=2, D=4 Fayet-Iliopoulos gauged supergravity was presented, and explicit solutions of various models containing one vector multiplet were constructed. Here we use the same method to find new nonextremal black holes to more complicated models. We also provide a general recipe to construct non-BPS extremal solutions for an arbitrary prepotential, as long as an axion-free condition holds. These follow from a set of first-order conditions, and are related to the corresponding supersymmetric black holes by a multiplication of the charge vector with a constant field rotation matrix S. The fake superpotential driving this first-order flow is nothing else than Hamilton's characteristic function in a Hamilton-Jacobi formalism, and coincides in the supersymmetric case (when S is plus or minus the identity) with the superpotential proposed by Dall'Agata and Gnecchi in arXiv:1012.3756. For the nonextremal black holes that asymptote to (magnetic) AdS, we compute both the mass coming from holographic renormalization and the one appearing in the superalgebra. The latter correctly vanishes in the BPS case, but also for certain values of the parameters that do not correspond to any known supersymmetric solution of N=2 gauged supergravity. We finally show that the product of all horizon areas depends only on the charges and the asymptotic value of the cosmological constant.