What can we learn about GW Physics with an elastic spherical antenna?

TL;DR

This paper develops a comprehensive formalism to analyze how elastic spherical antennas respond to gravitational waves, providing insights into detector sensitivity, cross sections, and directional deconvolution within general metric theories.

Contribution

It introduces a general formalism for elastic bodies' response to gravitational waves and applies it to spherical detectors, analyzing sensitivity, cross sections, and directional deconvolution.

Findings

Sensitivity parameters of spherical detectors are characterized.

Absorption cross sections are shown to be theory-independent.

Scaling properties of cross sections have implications for detector design.

Abstract

A general formalism is set up to analyse the response of an arbitrary solid elastic body to an arbitrary metric Gravitational Wave perturbation, which fully displays the details of the interaction antenna-wave. The formalism is applied to the spherical detector, whose sensitivity parameters are thereby scrutinised. A multimode transfer function is defined to study the amplitude sensitivity, and absorption cross sections are calculated for a general metric theory of GW physics. Their scaling properties are shown to be independent of the underlying theory, with interesting consequences for future detector design. The GW incidence direction deconvolution problem is also discussed, always within the context of a general metric theory of the gravitational field.