Slowly rotating black holes modeled by Solv geometries

TL;DR

This paper introduces a slowly rotating black hole solution in five-dimensional General Relativity with Solv horizon geometry, providing explicit solutions and analyzing its physical properties and phase space implications.

Contribution

It presents the first explicit slowly rotating black hole solution with Solv horizon geometry in five dimensions, expanding understanding of black hole solutions in this context.

Findings

Solution expressed via hypergeometric and exponential functions

Maintains asymptotic behavior of non-rotating black hole

Charges are computed and discussed in phase space context

Abstract

We present a slowly rotating generalization of a black hole modeled by a Solv horizon geometry, in five dimensional General Relativity. A separable ansatz compatible with Einstein equations is proposed, which is integrated in terms of hypergeometric and exponential functions. The solution highly simplifies after requiring to maintain the same asymptotic behaviour as the non-rotating black hole and to have finite, non-vanishing charges. We compute the charges of the solution and also comment on its importance for studying the phase space of the theory in this sector.