Environmental signatures in black hole ringdown within General Relativity

Recent studies of the quasinormal mode (QNM) spectra for black holes have revealed that small, far-field perturbations to the characteristic potential in the equation describing radial wave propagation produce many new modes which differ substantially in frequency from the QNMs of the unperturbed spacetime. However, the destabilized spectrum has not necessarily translated into significant differences in the time-domain ringdown signal. In this work, we extend this program to a more physically realistic scenario than a direct perturbation to the characteristic potential: a thin spherical shell of matter surrounding a Schwarzschild black hole. After accounting for the dynamics of the interaction between GWs and the matter shell in GR, we find a destabilized spectrum which features modes which do not converge to the unperturbed frequency in the limit of vanishing shell mass and use wave propagation arguments to explain the distribution of the new modes. Finally, we investigate the impact of such a physical QNM instability on a time-domain ringdown waveform by evaluating the performance of the full and rational ringdown filters proposed by (Ma et al., 2022) in removing the ringdown signature. We evaluate the structure of the modified QNM spectrum in the context of wave propagation physics in black hole spacetimes.