Generalization of the Regge-Wheeler equation for self-gravitating matter fields

It is shown that the dynamical evolution of perturbations on a static space time is governed by a standard pulsation equation for the extrinsic curvatu re tensor. The centerpiece of the pulsation equation is a wave operator who se spatial part is manifestly self-adjoint. In contrast to metric formulati ons, the curvature-based approach to perturbation theory generalizes in a n atural way to self-gravitating matter fields, including non-Abelian gauge f ields and perfect fluids. As an example, the pulsation equations for self-g ravitating, non-Abelian gauge fields are explicitly shown to be symmetric.