Covariant eigenmode overlap formalism for gravitational wave signals in electromagnetic cavities

TL;DR

This paper introduces a covariant formalism to analyze how gravitational waves interact with resonant electromagnetic and mechanical detectors, enabling improved modeling of high-frequency GW detection in microwave cavities.

Contribution

It develops a coordinate invariant eigenmode overlap formalism that accounts for damping and back-action effects, advancing the theoretical tools for GW detector design.

Findings

Provides a covariant eigenmode expansion method.

Derives coupling coefficients for high-frequency GW detectors.

Enables numerical modeling of arbitrary detector geometries.

Abstract

We develop a coordinate invariant formalism which describes the mechanical and electromagnetic interaction of gravitational waves (GWs) with a wide class of resonant detectors. We solve the GW-modified equations of electrodynamics and elasticity with dynamic boundary conditions using an eigenmode expansion. Furthermore, we take damping effects and electromagnetic back-action on mechanical systems covariantly into account. The resulting coupling coefficients are particularly useful for high-frequency gravitational wave experiments using microwave cavities and allow a straightforward numerical implementation for arbitrary detector geometries.