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arXiv · 1304.4683

Black-hole perturbation theory: The asymptotic spectrum of the prolate spin-weighted spheroidal harmonics

Shahar Hod
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Abstract

Prolate spin-weighted spheroidal harmonics play a key role in black-hole perturbation theory. In particular, the highly damped quasinormal resonances of rotating Kerr black holes are closely related to the asymptotic eigenvalues of these important functions. We here present a novel and compact derivation of the asymptotic eigenvalues of the prolate spin-weighted spheroidal harmonics. Our analysis is based on a simple trick which transforms the corresponding spin-weighted spheroidal angular equation into a Schrödinger-like wave equation which is amenable to a standard WKB analysis. Our analytical results for the prolate asymptotic spectrum agree with previous numerical computations of the eigenvalues which appear in the literature.

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Shahar Hod. 2013-04-17. Black-hole perturbation theory: The asymptotic spectrum of the prolate spin-weighted spheroidal harmonics. https://doi.org/10.1103/physrevd.87.064017

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