Quadratic Quasi-Normal Modes of a Schwarzschild Black Hole

Understand

Quadratic quasi-normal modes, 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 $\mathcal{R}\simeq0.154e^{-0.068i}$ for the most excited $\ell=4$ mode, matching results from Numerical Relativity.