Analytic Solutions of Teukolsky Equation in Kerr-de Sitter and Kerr-Newman-de Sitter Geometries

TL;DR

This paper derives explicit analytic solutions to the Teukolsky equation in Kerr-de Sitter and Kerr-Newman-de Sitter spacetimes, confirming their properties and identities, and clarifying normalization between solutions with different spins.

Contribution

It provides the first explicit analytic solutions for the Teukolsky equation in these geometries, verifying key identities and normalization conditions.

Findings

Solutions satisfy Teukolsky-Starobinsky identities

Normalization between spin-weighted solutions is established

Analytic solutions enhance understanding of black hole perturbations

Abstract

The analytic solution of Teukolsky equation in Kerr-de Sitter and Kerr-Newman-de Sitter geometries is presented and the properties of the solution are examined. In particular, we show that our solution satisfies the Teukolsky-Starobinsky identities explicitly and fix the relative normalization between solutions with the spin weight $s$ and $-s$.