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Conserved currents for Kerr and orthogonality of quasinormal modes

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arxiv 2210.15935 v3 pith:ENOCX34D submitted 2022-10-28 gr-qc

Stephen R. Green , Stefan Hollands , Laura Sberna , Vahid Toomani , Peter Zimmerman This is my paper · ORCID
classification gr-qc
keywords formbilinearkerrquasinormalconservedpropertiescurrentslocal
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abstract

We introduce a bilinear form for Weyl scalar perturbations of Kerr. The form is symmetric and conserved, and we show that, when combined with a suitable renormalization prescription involving complex r integration contours, quasinormal modes are orthogonal in the bilinear form for different (l, m, n). These properties are apparently not evident consequences of standard properties for the radial and angular solutions to the decoupled Teukolsky relations and rely on the Petrov type D character of Kerr and its t-$\phi$ reflection isometry. We show that quasinormal mode excitation coefficients are given precisely by the projection with respect to our bilinear form. These properties can make our bilinear form useful to set up a framework for nonlinear quasinormal mode coupling in Kerr. We also provide a general discussion on conserved local currents and their associated local symmetry operators for metric and Weyl perturbations, identifying a collection containing an increasing number of derivatives.

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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. Schr\"odinger perturbation theory for black hole quasinormal modes

    gr-qc 2026-07 conditional novelty 7.0 of 10

    A bilinear-form framework computes black-hole quasinormal-mode frequency shifts to any order, but the mode-sum expansion of the first-order mode shift diverges and needs a continuum piece.

  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. Relativistic Tidal Transitions of Saturated Kerr Boson Clouds

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    Relativistic Kerr wavefunctions change tidal transition matrix elements of saturated boson clouds by up to 21.7% relative to the hydrogenic approximation, with the radial profile responsible for ~80% of the change.

  4. Tidal perturbations of an extreme mass ratio inspiral around a Kerr black hole

    gr-qc 2026-01 conditional novelty 6.0 of 10

    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.

  5. Test-Field vs Physical Quasi-Normal Modes in Scalar-Tensor Theories

    gr-qc 2025-05 conditional novelty 6.0 of 10

    Test-field QNM spectra of BCL black holes deviate strongly from physical axial gravitational QNM spectra at high overtones, while fundamental modes remain close.

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