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Quadratic quasinormal modes of a Schwarzschild black hole

2024; American Physical Society; Volume: 110; Issue: 10 Linguagem: Inglês

10.1103/physrevd.110.104048

2470-0037

Bruno Bucciotti, Leonardo Juliano, Adrien Kuntz, Enrico Trincherini,

Black Holes and Theoretical Physics

Quadratic quasinormal mode, generated at second order in black hole perturbation theory, are a promising target for testing gravity in the nonlinear regime with next-generation gravitational wave detectors. While their frequencies have long been known, their amplitudes remain poorly studied. We introduce regular variables and compute amplitudes for Schwarzschild black holes with the Leaver algorithm. We find a nonlinear ratio $\mathcal{R}\ensuremath{\simeq}0.154{e}^{\ensuremath{-}0.068i}$ for the most excited $\ensuremath{\ell}=4$ mode, matching results from numerical relativity. We also predict new low-frequency $\ensuremath{\ell}=2$ quadratic modes.