Coupled gravitational and electromagnetic perturbations around a charged black hole

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Abstract
Coupled gravitational and electromagnetic perturbation equations are derived in the electrovacuum space around a charged rotating black hole using the Newman–Penrose formalism. When restricted to the nonrotating case, the equations separate in Schwarzschild coordinates. The asymptotic solutions at infinity and on the event horizon are obtained. In the coupled scattering of the electromagnetic and the gravitational waves on a Reissner–Nordström black hole, it is shown that the net energy flux is radially inward.