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Non-linear Quasi-Normal Modes of the Schwarzschild Black Hole from the Penrose Limit

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arxiv 2503.09350 v1 pith:EY6GZELU submitted 2025-03-12 gr-qc astro-ph.COhep-ph

Alex Kehagias , Davide Perrone , Antonio Riotto This is my paper
classification gr-qcastro-ph.COhep-ph
keywords blackholelimitmodesquasi-normalpenroseschwarzschildanalytically
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abstract

The Penrose limit connects a plane wave geometry to the photon ring of a black hole, where the quasi-normal modes are located in the eikonal limit. Utilizing this simplification, we analytically extract the quadratic-level non-linearities in the quasi-normal modes of a Schwarzschild black hole for the $(\ell\times\ell)\to 2\ell$ channel. We demonstrate that this result is independent of $\ell$ and further confirm it through symmetry arguments.

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Cited by 5 Pith papers

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

  1. 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.

  2. 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.

  3. Computing nonlinearity ratios using second order black hole perturbation theory

    gr-qc 2025-11 conditional novelty 6.0 of 10

    For the (2,2)×(2,2)→(4,4) channel, the WKB/matched-asymptotics scheme yields nonlinearity ratio 0.164 at infinity and 0.055 at the horizon, matching numerical relativity within its spread.

  4. The AdS Perspective on the Nonlinear Tails in Black Hole Ringdown

    gr-qc 2025-06 conditional novelty 5.0 of 10

    The known t^{-(2L+2)} nonlinear ringdown tail is rederived via AdS2 x S2, with a proposed but incorrectly normalized Aretakis amplitude relation.

  5. The Nonlinear Tails in Black Hole Ringdown: the Scattering Perspective

    gr-qc 2025-07 conditional novelty 4.0 of 10

    Nonlinear ringdown tails in the transverse-traceless gauge decay as t^{-(2ℓ+1)}, and this paper rederives that law from in-in scattering diagrams.

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