Rotating black holes in an expanding universe from fake supergravity

TL;DR

This paper constructs dynamical rotating black hole solutions within an expanding universe using fake supergravity techniques, extending known methods to cosmological contexts and exploring different base geometries.

Contribution

It introduces a method to generate rotating black holes in an expanding universe from fake supergravity, including solutions on various base spaces like flat, spherical, and Berger spheres.

Findings

Black hole solutions on flat and spherical bases are determined by harmonic functions.

Solutions on Berger sphere involve a deformed Laplace equation with squashing parameter.

Potential applications include studying black hole collisions and cosmic censorship violations.

Abstract

Using the recipe of arXiv:0902.4814, where all fake supersymmetric backgrounds of matter-coupled fake N=2, d=4 gauged supergravity were classified, we construct dynamical rotating black holes in an expanding FLRW universe. This is done for two different prepotentials that are both truncations of the stu model and correspond to just one vector multiplet. In this scenario, the cosmic expansion is driven by two U(1) gauge fields and by a complex scalar that rolls down its potential. Generically, the solutions of arXiv:0902.4814 are fibrations over a Gauduchon-Tod base space, and we make three different choices for this base, namely flat space, the three-sphere and the Berger sphere. In the first two cases, the black holes are determined by harmonic functions on the base, while in the last case they obey a deformed Laplace equation that contains the squashing parameter of the Berger sphere. This is the generalization to a cosmological context of the usual recipe in ungauged supergravity, where black holes are given in terms of harmonic functions on three-dimensional Euclidean space. The constructed solutions may be instrumental in addressing analytically questions like black hole collisions and violation of cosmic censorship.