Multimode gravitational wave detection: the spherical detector theory

TL;DR

This paper presents a comprehensive theoretical analysis of spherical gravitational wave detectors, highlighting their multi-mode capabilities and unique ability to independently measure all six GW amplitudes through their eigenmodes.

Contribution

The paper develops a first-principles theoretical framework for spherical GW detectors, explaining their multi-mode detection properties without relying on ad hoc assumptions.

Findings

Spherical detectors can independently measure all six GW amplitudes.

Eigenmodes of the sphere are matched to GW Riemann tensor components.

Theoretical model is supported by experimental evidence.

Abstract

A spherical gravity wave (GW) detector, unlike interferometers and bars, is a natural multi-mode device, i.e., it is capable of independently gathering information on all five quadrupole and one monopole amplitudes of a general incoming GW. This is because the sphere's degenerate oscillation eigenmodes are uniquely matched to the structure of the GWs' Riemann tensor components. Suitable linear combinations of the system readout channels completely deconvolve the six GW amplitudes. The present article is concerned with the theoretical reasons for the remarkable properties of a spherical GW detector. The analysis proceeds from first principles and is based on essentially no 'ad hoc' hypotheses. The mathematical beauty of the theory is outstanding, and abundant detail is given for a thorough understanding of the fundamental facts and ideas. Experimental evidence of the accuracy of the model is also provided, where possible.