Covariant eigenmode overlap formalism for gravitational wave signals in electromagnetic cavities

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.

arXiv commentV2: Correction to the surface normal perturbation in section 2 and further minor improvements throughout V3: Minor additional clarifications and typographical corrections. Equivalent to published version