Cosmological solutions from fake N=2 EYM supergravity

TL;DR

This paper characterizes fake supersymmetric solutions in Wick-rotated N=2 gauged supergravity with non-Abelian vectors, extending known cosmological black hole solutions and exploring null solutions with special holonomy.

Contribution

It provides a comprehensive classification of fake supersymmetric solutions in Wick-rotated N=2 supergravity, including generalizations of cosmological black holes and solutions with special holonomy.

Findings

Generalized cosmological black hole solutions with specific time dependence

Solutions with holonomy in Sim(2) in the null case

Some solutions are non-BPS solutions to N=2 supergravity

Abstract

We characterise the (fake) supersymmetric solutions of Wick-rotated N=2 d=4 gauged supergravity coupled to non-Abelian vector multiplets. In the time-like case we obtain generalisations of Kastor & Traschen's cosmological black holes: they have a specific time-dependence and the base-space must be 3-dimensional hyperCR/Gauduchon-Tod space. In the null-case, we find that the metric has a holonomy contained in Sim(2), give a general characterisation of the solutions, and give some examples. Finally, we point out that in some cases the solutions we found are non-BPS solutions to N=2 d=4 supergravity coupled to vector multiplets.