On the equations governing the perturbations of the Reissner–Nordström black hole

Abstract

By considering suitable combinations of the Weyl scalars and the spin coefficients, the basic equations governing the perturbations of the Reissner–Nordström black hole, in the Newman–Penrose formalism, are decoupled; a fundamental pair of decoupled equations are obtained. It is then shown how this pair of decoupled equations can be transformed into one dimensional wave equations which are appropriate for describing the perturbations of odd and of even parity. A simple relation is obtained which will allow derivation of a solution belonging to one parity from a solution belonging to the opposite parity. Finally, equations are derived in terms of which one can readily ascertain how an arbitrary superposition of gravitational and electromagnetic waves, incident on the black hole, will be reflected and absorbed.