title: Generalization of the regge-wheeler equation for self-gravitating matter fields
abstract: It is shown that the dynamical evolution of perturbations on a static spacetime is governed by a standard pulsation equation for the extrinsic curvature tensor. The centerpiece of the pulsation equation is a wave operator whose spatial part is manifestly self-adjoint. In contrast to metric formulations, the curvature-based approach to perturbation theory generalizes in a natural way to self-gravitating matter fields, including non-Abelian gauge fields and perfect fluids. As an example, the pulsation equations for self-gravitating, non-Abelian gauge fields are explicitly shown to be symmetric.
authors.affiliation: Max-Planck-Institute for Physics, Werner Heisenberg Institute, D-80805 Munich, Germany.
authors.initials: O
authors.lastname: Brodbeck
authors.initials: M
authors.lastname: Heusler
authors.initials: O
authors.lastname: Sarbach