Thursday, April 18, 2013

1304.4683 (Shahar Hod)

Black-hole perturbation theory: The asymptotic spectrum of the prolate
spin-weighted spheroidal harmonics
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Shahar Hod
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 Schr\"odinger-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.
View original: http://arxiv.org/abs/1304.4683

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