Pith. sign in

REVIEW 12 cited by

Second Order Quasi-Normal Mode of the Schwarzschild Black Hole

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 0708.0450 v1 pith:JVAFZKD7 submitted 2007-08-03 gr-qc astro-ph

Hiroyuki Nakano , Kunihito Ioka This is my paper · ORCID
classification gr-qcastro-ph
keywords ordersecondqnmsbinaryblackequationfirstgeneral
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We formulate and calculate the second order quasi-normal modes (QNMs) of a Schwarzschild black hole (BH). Gravitational wave (GW) from a distorted BH, so called ringdown, is well understood as QNMs in general relativity. Since QNMs from binary BH mergers will be detected with high signal-to-noise ratio by GW detectors, it is also possible to detect the second perturbative order of QNMs, generated by nonlinear gravitational interaction near the BH. In the BH perturbation approach, we derive the master Zerilli equation for the metric perturbation to second order and explicitly regularize it at the horizon and spatial infinity. We numerically solve the second order Zerilli equation by implementing the modified Leaver's continued fraction method. The second order QNM frequencies are found to be twice the first order ones, and the GW amplitude is up to $\sim 10%$ that of the first order for the binary BH mergers. Since the second order QNMs always exist, we can use their detections (i) to test the nonlinearity of general relativity, in particular the no-hair theorem, (ii) to remove fake events in the data analysis of QNM GWs and (iii) to measure the distance to the BH.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 12 Pith papers

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

  1. Early-Time Nonlinear Growth in an Unstable Q-Ball Hairy Black Hole

    gr-qc 2026-04 unverdicted novelty 7.0 of 10

    The early growth of the weakly responding scalar component in an unstable Q-ball hairy black hole is dominated by a second-order QNM sourced by the linear unstable mode, even while evolution remains perturbative.

  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. The Bondi--Sachs gauge, BMS frames, and memory in black hole perturbation theory

    gr-qc 2026-06 unverdicted novelty 6.0 of 10

    Introduces a gauge transformation framework for BMS frames in multiscale black hole perturbation theory on Kerr that incorporates memory effects and avoids infrared divergences.

  5. 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.

  6. Can Oscillatory and Persistent Nonlinearities Be Bridged in Black Hole Ringdown?

    gr-qc 2026-03 unverdicted novelty 6.0 of 10

    Quadratic quasinormal modes and the memory effect in black hole ringdown are related through bridge coefficients that depend primarily on remnant black hole parameters.

  7. Excitation factors for horizonless compact objects: long-lived modes, echoes, and greybody factors

    gr-qc 2025-11 unverdicted novelty 6.0 of 10

    Excitation factors of long-lived quasinormal modes in horizonless compact objects scale with their small imaginary frequency, suppressing early contributions and producing a hierarchy where prompt ringdown uses ordina...

  8. 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.

  9. Greybody factors, reflectionless scattering modes, and echoes of ultracompact horizonless objects

    gr-qc 2025-01 unverdicted novelty 5.0 of 10

    High-frequency quasi-reflectionless scattering modes in the greybody factors of ultracompact horizonless objects are responsible for echoes in the time-domain response.

  10. 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...

  11. 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.

  12. 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.

Pith tools