Torsion bar antenna in the proper reference frame with rotation

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.