Odd-parity stability of a Reissner-Nordström black hole

Abstract

The odd-parity perturbations of a Reissner-Nordstr\"om black hole are studied through the use of a variational principle for the perturbation equations. The Hamiltonian for the perturbations is expressed in terms of a natural set of canonical variables and shown to be (weakly) positive-definite. This result is used to prove the nonexistence of unstable normalmode solutions of the perturbation equations. The two wave equations governing gravitational and electromagnetic perturbations are decoupled by a simple transformation.