High-order asymptotics for the Spin-Weighted Spheroidal Equation at large real frequency

Abstract

The spin-weighted spheroidal eigenvalues and eigenfunctions arise in the separation by variables of spin-field perturbations of Kerr black holes. We derive a large, real-frequency asymptotic expansion of the spin-weighted spheroidal eigenvalues and eigenfunctions to high order. This expansion corrects and extends existing results in the literature and we validate it via a numerical calculation.

11 pages, 2 figures

References in corpus (3)

• Pade Approximants of the Green Function in Spherically Symmetric Spacetimes
• Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis
• High-order asymptotics for the Spin-Weighted Spheroidal Equation at large real frequency

Cited by in corpus (7)

• Tidal response and near-horizon boundary conditions for spinning exotic compact objects
• Exceptional point and hysteresis in perturbations of Kerr black holes
• High-order asymptotics for the Spin-Weighted Spheroidal Equation at large real frequency
• Spin wave optics for gravitational waves lensed by a Kerr black hole
• Massive scalar perturbations in Kerr Black Holes: near extremal analysis
• The Teukolsky--Starobinsky constants: facts and fictions
• Quasinormal mode frequencies of Kerr black holes from Regge trajectories