Linear perturbations of Kerr black hole in quadratic gravity

TL;DR

This paper develops a method to analyze linear perturbations of Kerr black holes within quadratic gravity, deriving decoupled equations that simplify understanding stability and dynamics in these modified theories.

Contribution

It introduces a novel approach combining Newman-Penrose formalism and Teukolsky-like equations to decouple perturbation equations in quadratic gravity on Kerr backgrounds.

Findings

Decoupled differential equations for Ricci tensor perturbations.

Application to Schwarzschild and Minkowski geometries.

Framework for stability analysis in quadratic gravity.

Abstract

Employing the Newman-Penrose formalism and following the classic Teukolsky-like approach, we linearise the field equations of quadratic gravity on the Kerr background and combine them with the linearised Ricci and Bianch identities. This leads to constraints on linear perturbations of the Kerr spacetime in quadratic gravity. The resulting differential equations are decoupled in such a way that only the Ricci tensor perturbations need to be found on the Kerr background in order to fully determine the solution. The results are illustrated in the simple non-trivial cases of the Schwarzschild and Minkowski geometries.