Self-adjoint wave equations for dynamical perturbations of self-gravitating fields

Abstract

It is shown that the dynamical evolution of linear perturbations on a static space-time is governed by a constrained wave equation for the extrinsic curvature tensor. The spatial part of the wave operator is manifestly elliptic and self-adjoint. In contrast to metric formulations, the curvature-based approach to gravitational perturbation theory generalizes in a natural way to self-gravitating matter fields. It is also demonstrated how to obtain symmetric pulsation equations for self-gravitating non-Abelian gauge fields, Higgs fields and perfect fluids. For vacuum fluctuations on a vacuum space-time, the Regge-Wheeler and Zerilli equations are rederived.

18 pages, no figures

References in corpus (2)

• The generalization of the Regge-Wheeler equation for self-gravitating matter fields
• Perturbation theory for self-gravitating gauge fields I: The odd-parity sector

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