Torsion bar antenna in the proper reference frame with rotation

TL;DR

This paper re-examines the response of a rotating torsion bar gravitational wave detector from a general-relativistic perspective, confirming its validity even when the gravitational wave frequency matches the antenna's rotation frequency.

Contribution

It provides a general-relativistic analysis of the torsion bar antenna's response, extending previous results to cases where gravitational wave and rotation frequencies are comparable.

Findings

Response remains valid when gravitational wave frequency is similar to rotation frequency.

General-relativistic formulation confirms previous results.

Analysis broadens understanding of rotating gravitational wave detectors.

Abstract

The resultant response of the rotating torsion bar antenna for gravitational waves discussed in [M. Ando et al., Phys. Rev. Lett. {\bf 105} (2010), 161101.] is re-investigate from a general-relativistic point of view. To do this, the equation of motion of a free falling particle in the proper reference frame of a rotating observer is used. As a result, the resultant response derived in the above paper is also valid even when $\omega_{g}\sim\Omega$, where $\omega_{g}$ and $\Omega$ are the angular frequencies of gravitational waves and the rotation of the antenna, respectively.