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Second order perturbations of a Schwarzschild black hole

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arxiv gr-qc/9510049 v2 pith:66XEBRPL submitted 1995-10-24 gr-qc astro-ph

Reinaldo Gleiser , Oscar Nicasio , Richard Price , Jorge Pullin This is my paper · ORCID
classification gr-qcastro-ph
keywords orderperturbationsblackfirstholeschwarzschildsecondsource
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abstract

We study the even-parity $\ell=2$ perturbations of a Schwarzschild black hole to second order. The Einstein equations can be reduced to a single linear wave equation with a potential and a source term. The source term is quadratic in terms of the first order perturbations. This provides a formalism to address the validity of many first order calculations of interest in astrophysics.

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Cited by 6 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. 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.

  3. 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.

  4. The impact of initial conditions on quasi-normal modes

    gr-qc 2024-12 conditional novelty 5.0 of 10

    Using an exactly solvable delta-function potential, the authors show linear quasi-normal mode amplitudes are generically time-dependent and derive stabilization times that can greatly exceed the usual 10 solar mass ru...

  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.

  6. Can We Detect Deviations from Einstein's Gravity in Black Hole Ringdowns?

    gr-qc 2024-11 conditional novelty 4.0 of 10

    Higher-derivative corrections to black hole ringdown spectra and quadratic modes are either absent or suppressed below detectability once causality is enforced, leaving Einstein's gravity as the sole observable description.

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