Gravito-electromagnetic approach for the space-time of a plane gravitational wave

Abstract

We build the Fermi frame associated to the world-line of a reference observer, arbitrary moving in a given space-time, and we show that local measurements can be described in terms of a gravito-electromagnetic analogy, where the gravito-electric and gravito-magnetic fields are related to the non inertial features of the observer’s motion and to the curvature of space-time. We apply this formalism to the space-time of a plane gravitational wave and show that the interaction of the wave with antennas can be explained in terms of gravito-electromagnetic forces acting on test masses. Moreover, we show that, besides the known gravito-electric effects, on which present gravitational waves antennas are based, gravito-magnetic effects could in principle lead to other kinds of detectors.