Phys. Rev. Lett. 84, 3033–3036 (2000)Generalization of the Regge-Wheeler Equation for Self-Gravitating Matter FieldsReceived 22 June 1999; published in the issue dated 3 April 2000 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. © 2000 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.84.3033
DOI:
10.1103/PhysRevLett.84.3033
PACS:
04.25.Nx, 04.40.-b
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