Gravitational waves in massive gravity: Waveforms generated by a particle plunging into a black hole and the excitation of quasinormal modes and quasibound states

TL;DR

This paper investigates gravitational wave emissions from a particle plunging into a black hole within massive gravity, analyzing quasinormal modes, quasibound states, and waveform features to test the theory's predictions.

Contribution

It constructs the resonance spectra and waveforms for a massive spin-2 field around a black hole, highlighting phenomena like quasibound state excitation and waveform regularization.

Findings

Quasibound states cause amplification and slow decay in the post-ringdown phase.

Waveforms during the adiabatic phase match those from particles on the innermost stable orbit.

Regularized waveforms agree well with unregularized spectra from quasinormal modes.

Abstract

With the aim of testing massive gravity in the context of black hole physics, we investigate the gravitational radiation emitted by a massive particle plunging into a Schwarzschild black hole from slightly below the innermost stable circular orbit. To do so, we first construct the quasinormal and quasibound resonance spectra of the spin-2 massive field for odd and even parity. Then, we compute the waveforms produced by the plunging particle and study their spectral content. This allows us to highlight and interpret important phenomena in the plunge regime, including (i) the excitation of quasibound states, with particular emphasis on the amplification and slow decay of the post-ringdown phase of the even-parity dipolar mode due to harmonic resonance; (ii) during the adiabatic phase, the waveform emitted by the plunging particle is very well described by the waveform emitted by the particle living on the innermost stable circular orbit, and (iii) the regularized waveforms and their unregularized counterparts constructed from the quasinormal mode spectrum are in excellent agreement. Finally, we construct, for arbitrary directions of observation and, in particular, outside the orbital plane of the plunging particle, the regularized multipolar waveforms, i.e., the waveforms constructed by summing over partial waveforms.