Separability of Gravitational Perturbation in Generalized Kerr-NUT-de Sitter Spacetime

TL;DR

This paper demonstrates that gravitational perturbations in generalized Kerr-NUT-de Sitter spacetime can be separated into simpler equations, aiding the analysis of stability and dynamics of these complex black hole solutions.

Contribution

It shows that a specific class of tensor perturbations in this spacetime admits separation of variables, transforming Einstein equations into Fuchsian ODEs.

Findings

Tensor perturbations allow separation of variables.

Perturbation equations reduce to Fuchs type ODEs.

Facilitates stability analysis of generalized Kerr-NUT-de Sitter spacetime.

Abstract

Generalized Kerr-NUT-de Sitter spacetime is the most general spacetime which admits a rank-2 closed conformal Killing-Yano tensor. It contains the higher-dimensional Kerr-de Sitter black holes with partially equal angular momenta. We study the separability of gravitational perturbations in the generalized Kerr-NUT-de Sitter spacetime. We show that a certain type of tensor perturbations admits the separation of variables. The linearized perturbation equations for the Einstein condition are transformed into the ordinary differential equations of Fuchs type.