High Frequency Asymptotics for the Spin-Weighted Spheroidal Equation

TL;DR

This paper derives a comprehensive asymptotic analysis for the solutions and eigenvalues of the spin-weighted spheroidal equation at high frequencies, supported by numerical validation.

Contribution

It provides a complete uniform asymptotic description for large frequency parameters, enhancing understanding of the equation's solutions.

Findings

Asymptotic formulas for eigenvalues and solutions at high frequencies

Numerical validation of the asymptotic results

Complete characterization of the behavior for fixed m

Abstract

We fully determine a uniformly valid asymptotic behaviour for large $a \omega$ and fixed $m$ of the angular solutions and eigenvalues of the spin-weighted spheroidal differential equation. We fully complement the analytic work with a numerical study.