The gravitational perturbations of the Kerr black hole I. The perturbations in the quantities which vanish in the stationary state

Abstract

As a preliminary towards a complete integration of the Newman-Penrose equations governing the gravitational perturbations of the Kerr black hole, the perturbations in the spin coefficients and in the components of the Weyl tensor, which vanish in the stationary state, are considered. The manner of treatment of the basic equations yields Teukolsky’s equations expressed directly in terms of the basic derivative operators of the theory and, further, suggests a preferred gauge in which two of the components of the Weyl tensor are governed by the same equations as a Maxwell field. Various identities and relations that are needed in subsequent work are assembled. In two appendixes, the solution of Maxwell’s equations in Kerr geometry and the perturbations of the charged Kerr-Newman black hole are considered.