Response of test masses to gravitational waves in the local Lorentz gauge

Abstract

The local Lorentz gauge represents a natural coordinate frame for an observer to analyze the effect of gravitational waves on detectors, and has been widely used to describe the response of resonant bars. Its application to laser interferometers has thus far been restricted to the long-wavelength regime, in which the separation between the test masses is much less than the wavelength of the gravitational waves. In this paper we show that the local Lorentz gauge can be used for calculations of geodesic deviations of the masses even when their separation is comparable to or greater than the wavelength of the gravitational waves. We find that a complete description of the gravitational waves in this gauge requires taking into account three different effects: displacements of the test masses, the gravitational redshift of light propagating between the masses, and variations in the rates of stationary clocks, all of which are induced by the gravitational wave. Only when taken together do these three effects represent a quantity which is translationally invariant and which can be observed in experiments. This translationally invariant quantity is identical to the response function calculated in the transverse traceless gauge.