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

作者：Hod Shahar^*

来源：Physical Review D - Particles, Fields, Gravitation and Cosmology, 2013, 87(6): 064017.

DOI：10.1103/PhysRevD.87.064017

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 Schrodinger-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. DOI: 10.1103/PhysRevD.87.064017

• 出版日期2013-3-14