Gravitational wave energy-momentum tensor and radiated power in a strongly curved background

TL;DR

This paper develops a method to define and compute the gravitational energy-momentum tensor in strongly curved backgrounds like Randall-Sundrum, enabling analysis of gravitational radiation in scenarios with large curvature.

Contribution

It introduces a covariantly-conserved gravitational energy-momentum tensor for strongly curved backgrounds, extending previous cosmological approaches to models like Randall-Sundrum.

Findings

Constructed gauge-invariant metric fluctuations in a strongly curved background.

Derived a formula for gravitational wave radiated power in such backgrounds.

Verified the formula in known cases.

Abstract

Allowing for the possibility of extra dimensions, there are two paradigms: either the extra dimensions are hidden from observations by being compact and small as in Kaluza-Klein scenarios, or the extra dimensions are large/non-compact and undetectable due to a large warping as in the Randall-Sundrum scenario. In the latter case, the five-dimensional background has a large curvature, and Isaacson's construction of the gravitational energy-momentum tensor, which relies on the assumption that the wavelength of the metric fluctuations is much smaller than the curvature length of the background spacetime, cannot be used. In this paper, we construct the gravitational energy-momentum tensor in a strongly curved background such as Randall-Sundrum. We perform a scalar-vector-tensor decomposition of the metric fluctuations with respect to the $SO(1,3)$ background isometry and construct the covariantly-conserved gravitational energy-momentum tensor out of the gauge-invariant metric fluctuations. We give a formula for the power radiated by gravitational waves and verify it in known cases. In using the gauge-invariant metric fluctuations to construct the gravitational energy-momentum tensor we follow previous work done in cosmology. Our framework has applicability beyond the Randall-Sundrum model.