Gravitational ringdown in the Minimal Theory of Massive Gravity

TL;DR

This paper investigates black hole perturbations in the Minimal Theory of Massive Gravity, demonstrating stability and differences in quasi-normal modes from General Relativity, which could be tested by future gravitational wave detectors like LISA.

Contribution

It introduces a novel first-order asymptotic method for computing black hole quasi-normal modes in MTMG, confirming stability and smooth GR limit.

Findings

Black holes in MTMG are stable.

Quasi-normal modes differ smoothly from GR.

Potential for testing MTMG with LISA.

Abstract

This work focuses on gravitational perturbations of black holes in the self-accelerating branch of the Minimal Theory of Massive Gravity (MTMG). This theory is a healthy extension of GR which displays the feature of massive tensor modes, without additional polarizations, strong-coupling issues nor requiring screening mechanisms. We proceed by implementing a newly developed technique that, instead of considering a second-order Schr\"odinger-like reformulation of perturbation equations, relies on a first-order formulation and solves it asymptotically, before numerically deriving the quasi-normal modes. We find that the black holes of MTMG are stable, and that their quasi-normal modes smoothly differ from the GR ones, for non-vanishing values of the graviton mass. This work hence confirms the fact that GR is a smooth limit of MTMG, and opens the exciting possibility of a clean test, performed for instance by the LISA detector.