Linearized propagation equations for metric fluctuations in a general (non-vacuum) background geometry

TL;DR

This paper derives the general linearized equations for metric fluctuations in non-vacuum backgrounds, highlighting how matter properties influence gravity wave propagation, with explicit examples for various matter sources.

Contribution

It provides a comprehensive derivation of metric perturbation equations in non-vacuum backgrounds and explores matter effects on gravitational wave propagation.

Findings

Matter stress tensor properties modify gravity wave behavior.

Explicit examples for fluid, scalar, and electromagnetic sources.

Framework applicable to cosmological and other non-vacuum scenarios.

Abstract

The linearized dynamical equation for metric perturbations in a fully general, non-vacuum, background geometry is obtained from the Hamilton variational principle applied to the action up to second order. We specialize our results to the case of traceless and transverse metric fluctuations, and we discuss how the intrinsic properties of the matter stress tensor can affect (and modify) the process of gravity wave propagation even in most conventional geometric scenarios, like (for instance) those described by a FLRW metric background. We provide explicit examples for fluid, scalar field and electromagnetic field sources.