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Second Order Perturbations of Kerr Black Holes: Reconstruction of the Metric

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arxiv 2008.11770 v2 pith:AEWCHMMF submitted 2020-08-26 gr-qc

Nicholas Loutrel , Justin L. Ripley , Elena Giorgi , Frans Pretorius This is my paper
classification gr-qc
keywords orderblackfirstkerrmetricproceduregravitationalhole
verification ladder T0 review T1 audit T2 compute T3 formal
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Motivated by gravitational wave observations of binary black hole mergers, we present a procedure to compute the leading order nonlinear gravitational wave interactions around a Kerr black hole. We describe the formalism used to derive the equations for second order perturbations. We develop a procedure that allows us to reconstruct the first order metric perturbation solely from knowledge of the solution to the first order Teukolsky equation, without the need of Hertz potentials. Finally, we illustrate this metric reconstruction procedure in the asymptotic limit for the first order quasi-normal modes of Kerr. In a companion paper, we present a numerical implementation of these ideas.

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Cited by 7 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. Tidal perturbations of an extreme mass ratio inspiral around a Kerr black hole

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    A closed-form Kerr metric under slow quadrupolar tides yields spin-dependent tidal shifts of the ISCO and light ring, with larger shifts for retrograde orbits around fast-spinning holes.

  4. Twisting asymptotically-flat spacetimes

    gr-qc 2025-11 conditional novelty 6.0 of 10

    Twisting asymptotically-flat spacetimes are brought into a generalized Bondi gauge with finite radial expansion, producing new flux-balance laws, Carroll-boost symmetries, and finite supertranslated Kerr–Taub–NUT metrics.

  5. Gravitational Enstrophy: Local Geometric Origin and Inverse-Cascade Constraints

    gr-qc 2026-08 conditional novelty 5.0 of 10

    General relativity admits a magnetic Weyl enstrophy whose approximate conservation, together with energy, enforces a gravitational Fjørtoft constraint biasing nonlinear energy transfer toward lower frequencies in near...

  6. 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.

  7. 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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