Kerr-(Anti-)de Sitter Black Holes: Perturbations and quasi-normal modes in the slow rotation limit

TL;DR

This paper derives analytical formulas for the fundamental quasi-normal mode frequencies of scalar, vector, and tensor perturbations in slowly rotating Kerr-(Anti-)de Sitter black holes, confirming their accuracy against numerical results.

Contribution

It provides new Schrödinger-style master equations and analytical expressions for quasi-normal modes in the slow rotation limit of Kerr-(Anti-)de Sitter black holes, extending previous results.

Findings

Analytical quasi-normal mode frequencies agree with numerical calculations.

Axial and polar gravitational frequencies are isospectral to linear order in spin, except when both spin and cosmological constant are non-zero.

Derived master equations are valid up to linear order in black hole spin.

Abstract

We study the perturbations of scalar, vector, and tensor fields in a slowly rotating Kerr-(Anti-)de Sitter black hole spacetime, presenting new and existing Schr\"odinger style master equations for each type of perturbation up to linear order in black hole spin $a$. For each type of field we calculate analytical expressions for the fundamental quasi-normal mode frequencies. These frequencies are compared to existing results for Schwarzschild-de Sitter, slowly rotating Kerr, and slowly rotating Kerr-de Sitter black holes. In all cases good agreement is found between the analytic expressions and those frequencies calculated numerically. In addition, the axial and polar gravitational frequencies are shown to be isospectral to linear order in $a$ for all cases other than for both non-zero $a$ and $\Lambda$.