Refined Error Estimates for the Riccati Equation with Applications to the Angular Teukolsky Equation

TL;DR

This paper develops refined error estimates for approximate solutions of Riccati and Sturm-Liouville equations, applying these to the angular Teukolsky equation in Kerr black hole geometry.

Contribution

It introduces new rigorous error bounds for classical approximation methods and applies them to complex potentials in black hole physics.

Findings

Refined error estimates improve accuracy of approximate solutions.

Application to Kerr geometry demonstrates practical relevance.

Enhanced understanding of angular Teukolsky equation solutions.

Abstract

We derive refined rigorous error estimates for approximate solutions of Sturm-Liouville and Riccati equations with real or complex potentials. The approximate solutions include WKB approximations, Airy and parabolic cylinder functions, and certain Bessel functions. Our estimates are applied to solutions of the angular Teukolsky equation with a complex aspherical parameter in a rotating black hole Kerr geometry.