Quadratic Quasi-Normal Modes of a Schwarzschild Black Hole

Abstract

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 $\mathcal{R}\simeq 0.154e^{-0.068i}$ for the most excited $\ell =4$ mode, matching results from Numerical Relativity. We also predict new low-frequency $\ell =2$ quadratic modes.

5 pages, 2 figures. v2: matches published version

References in corpus (30)

• Inspiral, merger and ring-down of equal-mass black-hole binaries
• Inspiral, merger and ringdown of unequal mass black hole binaries: a multipolar analysis
• Matched-filtering and parameter estimation of ringdown waveforms
• Nonlinearities in Black Hole Ringdowns
• Nonlinear effects in black hole ringdown
• Agnostic black hole spectroscopy: Quasinormal mode content of numerical relativity waveforms and limits of validity of linear perturbation theory
• Ringdown overtones, black hole spectroscopy, and no-hair theorem tests
• Constraints on quasi-normal-mode frequencies with LIGO-Virgo binary-black-hole observations
• Spectroscopy of binary black hole ringdown using overtones and angular modes
• Second Order Quasi-Normal Mode of the Schwarzschild Black Hole
• Extracting linear and nonlinear quasinormal modes from black hole merger simulations
• Parametrized ringdown spin expansion coefficients: a data-analysis framework for black-hole spectroscopy with multiple events
• Generation and propagation of nonlinear quasi-normal modes of a Schwarzschild black hole
• Quasinormal-mode filters: a new approach to analyze the gravitational-wave ringdown of binary black-hole mergers
• A complete gauge-invariant formalism for arbitrary second-order perturbations of a Schwarzschild black hole
• Second and higher-order quasi-normal modes in binary black hole mergers
• Second and higher-order perturbations of a spherical spacetime
• Spin dependence of black hole ringdown nonlinearities
• The excitation of quadratic quasinormal modes for Kerr black holes
• High-order gauge-invariant perturbations of a spherical spacetime
• Nonlinear ringdown at the black hole horizon
• Non-linear Black Hole Ringdowns: an Analytical Approach
• Nonlinear quasinormal mode detectability with next-generation gravitational wave detectors
• Black hole spectroscopy horizons for current and future gravitational wave detectors
• Spectroscopic analysis of stellar mass black-hole mergers in our local universe with ground-based gravitational wave detectors
• Nonlinear Quasi-Normal Modes: Uniform Approximation
• Quasinormal modes and their excitation beyond general relativity
• A parametrized quasi-normal mode framework for non-Schwarzschild metrics
• Parametrized Black Hole Quasinormal Ringdown Formalism for Higher Overtones
• Amplitudes and Polarizations of Quadratic Quasi-Normal Modes for a Schwarzschild Black Hole

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