Noether and Belinfante corrected types of currents for perturbations in the Einstein-Gauss-Bonnet gravity

TL;DR

This paper derives covariant conserved currents for perturbations in Einstein-Gauss-Bonnet gravity using Noether and Belinfante methods, with applications to gravitational waves and radiating black holes in higher dimensions.

Contribution

It provides explicit covariant formulas for conserved currents in EGB gravity for arbitrary perturbations and backgrounds, extending previous methods to this theory.

Findings

Energy density for weak gravitational waves in D-dimensional EGB gravity.

Mass flux for 3D radiating black holes in 6D EGB gravity.

Explicit covariant expressions for perturbation currents in EGB theory.

Abstract

In the framework of an arbitrary $D$-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 N{\oe}ther 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 $D$-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.