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.
- Received 22 June 1999
DOI:https://doi.org/10.1103/PhysRevLett.84.3033
©2000 American Physical Society