Interaction of gravitational waves with matter

TL;DR

This paper presents a unified formalism to describe how gravitational waves interact with matter, deriving a general dispersion relation and analyzing contributions similar to electromagnetic self energy, with applications to various systems.

Contribution

It introduces a novel formalism that separates gravitational effects from matter interactions and derives a general dispersion expression in flat spacetime.

Findings

Derived a general dispersion relation for gravitational waves in matter.

Identified paramagnetic and diamagnetic contributions to gravitational wave self energy.

Applied the formalism to free particles, scalar fields, and fermionic superfluids.

Abstract

We develop a unified formalism for describing the interaction of gravitational waves with matter that clearly separates the effects of general relativity from those due to interactions in the matter. Using it, we derive a general expression for the dispersion of gravitational waves in matter in terms of correlation functions for the matter in flat spacetime. The self energy of a gravitational wave is shown to have contributions analogous to the paramagnetic and diamagnetic contributions to the self energy of an electromagnetic wave. We apply the formalism to some simple systems - free particles, an interacting scalar field, and a fermionic superfluid.