Charged black holes: Wave equations for gravitational and electromagnetic perturbations

TL;DR

This paper derives wave equations for electromagnetic and gravitational perturbations of charged Kerr black holes using a new gauge and curvature derivatives, advancing understanding of black hole stability.

Contribution

It introduces a novel derivation of wave equations for perturbations in charged Kerr black holes employing a new gauge and curvature derivatives.

Findings

Derived wave equations for electromagnetic and gravitational perturbations.

Utilized a new gauge based on derivatives of the first curvature of a null direction.

Provides a framework for analyzing black hole stability and perturbations.

Abstract

A pair of wave equations for the electromagnetic and gravitational perturbations of the charged Kerr black hole are derived. The perturbed Einstein-Maxwell equations in a new gauge are employed in the derivation. The wave equations refer to the perturbed Maxwell spinor $\Phi_0$ and to the shear $\sigma$ of a principal null direction of the Weyl curvature. The whole construction rests on the tripod of three distinct derivatives of the first curvature $\kappa$ of a principal null direction.