Instability of black holes in massive gravity

TL;DR

This paper demonstrates that black holes in massive gravity theories are linearly unstable due to a Gregory-Laflamme type instability, suggesting static black holes may not exist in such theories, especially at cosmological scales.

Contribution

It shows the presence of Gregory-Laflamme instability in black holes within ghost-free massive bi-gravity theories, highlighting potential non-existence of static black holes in these models.

Findings

Unstable mode found in bi-Schwarzschild solutions.

Instability timescale comparable to Hubble time for small graviton mass.

Results apply to both single and bi-metric massive gravity theories.

Abstract

We show that linear perturbations around the simplest black hole solution of massive bi-gravity theories, the bi-Schwarzschild solution, exhibit an unstable mode featuring the Gregory-Laflamme instability of higher-dimensional black strings. The result is obtained for the massive gravity theory which is free from the Boulware-Deser ghost, as well as for its extension with two dynamical metrics. These results may indicate that static black holes in massive gravity do not exist. For graviton mass of order of Hubble scale, however, the instability timescale is of order of the Hubble time.