A hollow sphere as a detector of gravitational radiation

TL;DR

This paper analyzes how hollow spherical detectors can effectively detect gravitational waves, offering a design with low resonance frequencies and large cross sections that complement existing interferometers.

Contribution

It provides an analytical solution for the normal mode spectrum and response of hollow spheres to gravitational waves, highlighting their potential as omnidirectional detectors.

Findings

Hollow spheres can be designed with low resonance frequencies (~200 Hz).

They maintain large energy absorption cross sections.

Their frequency range overlaps with large interferometers.

Abstract

The most important features of the proposed spherical gravitational wave detectors are closely linked with their symmetry. Hollow spheres share this property with solid ones, considered in the literature so far, and constitute an interesting alternative for the realization of an omnidirectional gravitational wave detector. In this paper we address the problem of how a hollow elastic sphere interacts with an incoming gravitational wave and find an analytical solution for its normal mode spectrum and response, as well as for its energy absorption cross sections. It appears that this shape can be designed having relatively low resonance frequencies (about 200 Hz) yet keeping a large cross section, so its frequency range overlaps with the projected large interferometers. We also apply the obtained results to discuss the performance of a hollow sphere as a detector for a variety of gravitational wave signals.