Noether and Belinfante corrected types of currents for perturbations in the Einstein-Gauss-Bonnet gravity
arXiv:1102.5636 · doi:10.1088/0264-9381/28/21/215021
Abstract
In the framework of an arbitrary -dimensional metric theory, perturbations are considered on arbitrary backgrounds that are however solutions of the theory. Conserved currents for perturbations are presented following two known prescriptions: canonical Nœther theorem and Belinfante symmetrization rule. Using generalized formulae, currents in the Einstein-Gauss-Bonnet (EGB) gravity for arbitrary types of perturbations on arbitrary curved backgrounds (not only vacuum) are constructed in an explicit covariant form. Special attention is paid to the energy-momentum tensors for perturbations which are an important part in the structure of the currents. We use the derived expressions for two applied calculations: a) to present the energy density for weak flat gravitational waves in -dimensional EGB gravity; b) to construct the mass flux for the Maeda-Dadhich-Molina 3D radiating black holes of a Kaluza-Klein type in 6D EGB gravity.
22 pages, no figures, version accepted to CQG
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- Canonical Noether and the energy-momentum non-uniqueness problem in linearized gravity
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- Einstein-Katz action, variational principle, Noether charges and the thermodynamics of AdS-black holes
- Noether symmetries for fields and branes in backgrounds with Killing vectors