Self-adjoint wave equations for dynamical perturbations of self-gravitating fields - art. no. 104015

It is shown that the dynamical evolution of linear perturbations on a stati c space-time is governed by a constrained wave equation for the extrinsic c urvature tensor. The spatial part of the wave operator is manifestly ellipt ic and self-adjoint. In contrast with metric formulations, the curvature-ba sed approach to gravitational perturbation theory generalizes in a natural way to self-gravitating matter fields. It is also demonstrated how to obtai n symmetric pulsation equations for self-gravitating non-Abelian gauge fiel ds, Higgs fields and perfect fluids. For vacuum fluctuations on a vacuum sp ace-time, the Regge-Wheeler and Zerilli equations are rederived.