Compact Gravity Wave Detector

Abstract

An incoming gravity wave being a stress wave is a surface with intrinsic curvature. When a light beam is parallel transported on this non-Euclidian surface it acquires an excess phase which accumulates with each curcuit. We calculate the separate contributions to excess phase from the wave geometry as well as the dynamic response of mirrors in a Michelson interferometer. Using these results and a combination of analogue and digital signal processing techniques we show how a compact interferometer can be made sensitive to gravity waves of amplitude density $10^{-23}/\sqrt{Hz}$ within a frequency range $10^{-4}Hz$ to $10^4Hz$. As an example we describe a 10cm Michelson interferometer designed to measure gravity waves from sources as far as the Virgo cluster.