Rotating black holes in massive gravity

TL;DR

This paper introduces rotating black hole solutions in massive gravity, extending known solutions to include charge and bi-gravity cases, with metrics expressed in advanced Eddington-Finkelstein coordinates.

Contribution

It provides explicit rotating black hole solutions in massive gravity and bi-gravity theories, including charged cases, which were not previously available.

Findings

Solutions expressed in advanced Eddington-Finkelstein coordinates

Physical metric has Kerr form, fiducial metric is flat or Kerr-like

Charged rotating black hole solutions analogous to Kerr-Newman

Abstract

We present a solution for rotating black holes in massive gravity. We first give a solution of massive gravity with one dynamical metric. Both metrics of this solution are expressed in the advanced Eddington-Finkelstein-like coordinates: the physical metric has the original Kerr line element, while the fiducial metric is flat, but written in a rotating Eddington-Finkelstein form. For the bi-gravity theory we give an analogue of this solution: the two metrics have the original Kerr form, but, in general, different black hole masses. The generalisation of the solution to include the electric charge is also given, it is an analogue of the Kerr-Newman solution in General Relativity. We also discuss further possible ways to generalise the solutions.