Dixon's extended bodies and weak gravitational waves

General relativity considers Dixon’s theory as the standard theory to deal with the motion of extended bodies in a given gravitational background. We discuss here the features of the “reaction” of an extended body to the passage of a weak gravitational wave. We find that the body acquires a dipolar moment induced by its quadrupole structure. Furthermore, we derive the “world function” for the weak field limit of a gravitational wave background and use it to estimate the deviation between geodesics and the world lines of structured bodies. Measuring such deviations, due to the existence of cumulative effects, should be favorite with respect to measuring the amplitude of the gravitational wave itself.