Waveforms in massive gravity and neutralization of giant black hole ringings

TL;DR

This paper investigates gravitational wave signals from black holes in massive gravity, revealing that certain giant ringings are neutralized by quasibound states and evanescent modes, but still produce observable, slowly decaying waveforms.

Contribution

It demonstrates that giant black hole ringings predicted in massive gravity are neutralized by quasibound states and evanescent modes, providing a clearer understanding of gravitational wave signatures.

Findings

Giant ringings are neutralized in waveforms due to quasibound states and evanescent modes.

Waveforms remain pronounced and slowly decaying, dominated by long-lived quasibound states.

Low graviton mass leads to clean, ordinary ringing signatures in waveforms.

Abstract

A distorted black hole radiates gravitational waves in order to settle down in a smoother geometry. During that relaxation phase, a characteristic damped ringing is generated. It can be theoretically constructed from both the black hole quasinormal frequencies (which govern its oscillating behavior and its decay) and the associated excitation factors (which determine intrinsically its amplitude) by carefully taking into account the source of the distortion. In the framework of massive gravity, the excitation factors of the Schwarzschild black hole have an unexpected strong resonant behavior which, theoretically, could lead to giant and slowly decaying ringings. If massive gravity is relevant to physics, one can hope to observe these extraordinary ringings by using the next generations of gravitational wave detectors. Indeed, they could be generated by supermassive black holes if the graviton mass is not too small. In fact, by focusing on the odd-parity $\ell=1$ mode of the Fierz-Pauli field, we shall show here that such ringings are neutralized in waveforms due to (i) the excitation of the quasibound states of the black hole and (ii) the evanescent nature of the particular partial modes which could excite the concerned quasinormal modes. Despite this, with observational consequences in mind, it is interesting to note that the waveform amplitude is nevertheless rather pronounced and slowly decaying (this effect is now due to the long-lived quasibound states). It is worth noting also that, for very low values of the graviton mass (corresponding to the weak instability regime for the black hole), the waveform is now very clean and dominated by an ordinary ringing which could be used as a signature of massive gravity.