On Black Holes in Massive Gravity

TL;DR

This paper presents an exact black hole solution in massive gravity that transitions to de Sitter space at large scales, avoiding horizon singularities seen in Minkowski solutions, and highlights the necessity of nontrivial St"uckelberg fields.

Contribution

The authors derive a novel analytic black hole solution in massive gravity with a large-scale de Sitter transition, addressing horizon singularities and expanding understanding of black holes in modified gravity theories.

Findings

Black hole solutions with de Sitter asymptotics in massive gravity.

Horizon singularities are avoided with nontrivial St"uckelberg fields.

Solutions are limited to specific parameter values but suggest broader applicability.

Abstract

In massive gravity the so-far-found black hole solutions on Minkowski space happen to convert horizons into a certain type of singularities. Here we explore whether these singularities can be avoided if space-time is not asymptotically Minkowskian. We find an exact analytic black hole (BH) solution which evades the above problem by a transition at large scales to self-induced de Sitter (dS) space-time, with the curvature scale set by the graviton mass. This solution is similar to the ones discovered by Koyama, Niz and Tasinato, and by Nieuwenhuizen, but differs in detail. The solution demonstrates that in massive GR, in the Schwarzschild coordinate system, a BH metric has to be accompanied by the St\"uckelberg fields with nontrivial backgrounds to prevent the horizons to convert into the singularities. We also find an analogous solution for a Reissner-Nordstr\"om BH on dS space. A limitation of our approach, is that we find the solutions only for specific values of the two free parameters of the theory, for which both the vector and scalar fluctuations loose their kinetic terms, however, we hope our solutions represent a broader class with better behaved perturbations.