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Amplitudes and Polarizations of Quadratic Quasi-Normal Modes for a Schwarzschild Black Hole

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arxiv 2406.14611 v2 pith:WTLODF3E submitted 2024-06-20 hep-th astro-ph.HEgr-qc

Bruno Bucciotti , Leonardo Juliano , Adrien Kuntz , Enrico Trincherini This is my paper
classification hep-thastro-ph.HEgr-qc
keywords modesamplitudeslinearquadraticpolarizationsblackconditionsfour
verification ladder T0 review T1 audit T2 compute T3 formal
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General Relativity predicts the existence of quadratic quasi-normal modes at second order in perturbation theory. Building on our recent work, we compute the amplitudes and polarizations of these modes for non-rotating black holes, showing that they are completely determined by the amplitudes and polarizations of linear modes. We obtain the ratio of quadratic to linear amplitudes, which still depends on the initial conditions of the merger through the polarization of linear modes. However, we demonstrate that this dependence is captured by four fundamental numbers, independent of initial conditions, representing four different combinations of linear modes parities. Additionally, we prove two selection rules regarding the vanishing of classes of quadratic modes. Our results are available online as a package which provides the ratio of amplitudes across a broad spectrum of angular momenta.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Probing Direct Waves in Black Hole Ringdowns

    gr-qc 2025-09 conditional novelty 7.0 of 10

    Merger gravitational wave signals contain a 'direct wave' from the plunging companions, screened by the remnant's potential, with frequency near the superradiant value for high-spin remnants and SNR above 10 in GW1509...

  2. Perturbations of Plane Waves and Quadratic Quasinormal Modes on the Lightring

    gr-qc 2025-09 conditional novelty 7.0 of 10

    Second-order gravitational perturbations on plane waves are solved with a GHP master equation and tensor harmonics, yielding quadratic quasinormal mode ratios and selection rules.

  3. Nonlinearities in Kerr Black Hole Ringdown from the Penrose Limit

    gr-qc 2025-07 conditional novelty 7.0 of 10

    Kerr quadratic quasi-normal mode amplitudes and phases are computed analytically in the eikonal limit via the Penrose limit, giving an explicit spin-dependent nonlinearity ratio.

  4. GW250114 reveals black hole horizon signatures

    gr-qc 2025-10 conditional novelty 6.0 of 10

    The merger signal of GW250114 contains a residual 'direct wave' component whose frequency and damping match the remnant horizon's rotation frequency and surface gravity.

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