The Design Strain Sensitivity of the Schenberg Spherical Resonant Antenna for Gravitational Waves

TL;DR

This paper reviews the Schenberg spherical resonant antenna's transfer function and recalculates its strain sensitivity for gravitational wave detection, comparing it to existing detectors and exploring its potential for alternative detection principles.

Contribution

It provides a detailed analysis of the Schenberg antenna's transfer function and recalculates its strain sensitivity considering degenerate and non-degenerate cases, highlighting its potential and limitations.

Findings

Ultimate sensitivity near the quantum limit.

Current sensitivity comparable to LIGO O3 results.

Potential for alternative gravitational wave detection methods.

Abstract

The main purpose of this study is to review the Schenberg resonant antenna transfer function and to recalculate the antenna design strain sensitivity for gravitational waves. We consider the spherical antenna with six transducers in the semi dodecahedral configuration. When coupled to the antenna, the transducer-sphere system will work as a mass-spring system with three masses. The first one is the antenna effective mass for each quadrupole mode, the second one is the mass of the mechanical structure of the transducer first mechanical mode and the third one is the effective mass of the transducer membrane that makes one of the transducer microwave cavity walls. All the calculations are done for the degenerate (all the sphere quadrupole mode frequencies equal) and non-degenerate sphere cases. We have come to the conclusion that the 'ultimate' sensitivity of an advanced version of Schenberg antenna (aSchenberg) is around the standard quantum limit (although the parametric transducers used could, in principle, surpass this limit). However, this sensitivity, in the frequency range where Schenberg operates, has already been achieved by the two aLIGOs in the O3 run, therefore, the only reasonable justification for remounting the Schenberg antenna and trying to place it in the sensitivity of the standard quantum limit would be to detect gravitational waves with another physical principle, different from the one used by laser interferometers. This other physical principle would be the absorption of the gravitational wave energy by a resonant mass like Schenberg.