Partially massless gravitons do not destroy general relativity black holes

TL;DR

This paper demonstrates that in partially massless gravity, black holes known from general relativity remain stable, and the spectrum of gravitational perturbations is identical to that in Einstein's theory, highlighting a unique stability feature.

Contribution

It shows that partially massless gravity preserves the stability of black holes and maintains an isospectral perturbation spectrum, unlike other massive gravity theories.

Findings

Black holes are stable in partially massless gravity.

The perturbation spectrum is identical to that of general relativity.

Partially massless gravity features a fixed graviton mass related to the cosmological constant.

Abstract

Recent nonlinear completions of Fierz-Pauli theory for a massive spin-2 field include nonlinear massive gravity and bimetric theories. The spectrum of black-hole solutions in these theories is rich, and comprises the same vacuum solutions of Einstein's gravity enlarged to include a cosmological constant. It was recently shown that Schwarzschild (de Sitter) black holes in these theories are generically unstable against spherical perturbations. Here we show that a notable exception is partially massless gravity, where the mass of the graviton is fixed in terms of the cosmological constant by \mu^2=2\Lambda/3 and a new gauge invariance emerges. We find that general-relativity black holes are stable in this limit. Remarkably, the spectrum of massive gravitational perturbations is isospectral.