Charged black holes: Wave equations for gravitational and electromagnetic 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 $\hat{I}{¦}_0$ and to the shear $\ddot{I}ƒ$ of a principal null direction of the Weyl curvature. The whole construction rests on the tripod of three distinct derivatives of the first curvature $\hat{I}º$ of a principal null direction.

12 pages, to appear in Ap.J