Perturbations of the almost Killing equation and their implications
arXiv:2011.13955 · doi:10.1103/PhysRevD.103.084020
Abstract
Killing vectors play a crucial role in characterizing the symmetries of a given spacetime. However, realistic astrophysical systems are in most cases only approximately symmetric. Even in the case of an astrophysical black hole, one might expect Killing symmetries to exist only in an approximate sense due to perturbations from external matter fields. In this work, we consider the generalized notion of Killing vectors provided by the almost Killing equation, and study the perturbations induced by a perturbation of a background spacetime satisfying exact Killing symmetry. To first order, we demonstrate that for nonradiative metric perturbations (that is, metric perturbations with nonvanishing trace) of symmetric vacuum spacetimes, the perturbed almost Killing equation avoids the problem of an unbounded Hamiltonian for hyperbolic parameter choices. For traceless metric perturbations, we obtain similar results for the second-order perturbation of the almost Killing equation, with some additional caveats. Thermodynamical implications are also explored.
21 pages. Matches published version
References in corpus (8)
- Covariance properties and regularization of conserved currents in tetrad gravity
- Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry
- Conservation laws in gravitational theories with general nonminimal coupling
- Conservation laws in gravity: A unified framework
- Approximate spacetime symmetries and conservation laws
- Conserved currents in gravitational models with quasi-invariant Lagrangians: Application to teleparallel gravity
- Komar fluxes of circularly polarized light beams and cylindrical metrics
- Almost-Killing equation: Stability, hyperbolicity, and black hole Gauss law