BPS black holes in N=2 D=4 gauged supergravities

TL;DR

This paper constructs and analyzes BPS black hole solutions in gauged N=2, D=4 supergravity, exploring scalar hair, symmetry breaking, and ghost issues, with explicit examples and potential fermionic hair solutions.

Contribution

It introduces new BPS black hole solutions in gauged N=2 supergravity, including cases with scalar hair and methods to address ghost problems.

Findings

Existence of BPS black holes with scalar hair under specific conditions

Solutions include asymptotically flat and anti-de Sitter cases

Ghost-like scalars appear in certain symmetric solutions

Abstract

We construct and analyze BPS black hole solutions in gauged N=2, D=4 supergravity with charged hypermultiplets. A class of solutions can be found through spontaneous symmetry breaking in vacua that preserve maximal supersymmetry. The resulting black holes do not carry any hair for the scalars. We demonstrate this with explicit examples of both asymptotically flat and anti-de Sitter black holes. Next, we analyze the BPS conditions for asymptotically flat black holes with scalar hair and spherical or axial symmetry. We find solutions only in cases when the metric contains ripples and the vector multiplet scalars become ghost-like. We give explicit examples that can be analyzed numerically. Finally, we comment on a way to circumvent the ghost-problem by introducing also fermionic hair.