2003ApJ...582..342P

A pair of wave equations for the electromagnetic and gravitational perturbations of a 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 Φ₀and to the shear σ of a principal null direction of the Weyl curvature. The whole construction rests on the tripod of three distinct derivatives of the first curvature κ of a principal null direction.