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Second and higher-order perturbations of a spherical spacetime

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arxiv gr-qc/0607025 v1 pith:3PDEWXKO submitted 2006-07-06 gr-qc

David Brizuela , Jose M. Martin-Garcia , Guillermo A. Mena Marugan This is my paper
classification gr-qc
keywords equationsgivenperturbationssphericalarbitraryformalismgeneralizedperturbation
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The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order, spherical and nonspherical perturbations around an arbitrary spherical spacetime is generalized to higher orders, focusing on second-order perturbation theory. The GS harmonics are generalized to an arbitrary number of indices on the unit sphere and a formula is given for their products. The formalism is optimized for its implementation in a computer algebra system, something that becomes essential in practice given the size and complexity of the equations. All evolution equations for the second-order perturbations, as well as the conservation equations for the energy-momentum tensor at this perturbation order, are given in covariant form, in Regge-Wheeler gauge.

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Cited by 3 Pith papers

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

  1. Black Hole Ringdown Nonlinearities in the Large-D Limit

    gr-qc 2026-06 unverdicted novelty 6.0 of 10

    In the large-D limit, analytic third-order nonlinear corrections to quasinormal modes improve ringdown modeling accuracy by several orders of magnitude for head-on black hole collisions.

  2. 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.

  3. 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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