Dixon's extended bodies and weak gravitational waves

TL;DR

This paper explores how extended bodies in general relativity respond to weak gravitational waves, revealing induced dipole moments and deviations from geodesic motion, which could aid gravitational wave detection.

Contribution

It analyzes the reaction of extended bodies to weak gravitational waves using Dixon's theory, deriving the world function, and proposing a new method to measure gravitational wave effects.

Findings

Extended bodies acquire dipolar moments due to quadrupole structure.

Deviations from geodesics can be used to detect gravitational waves.

Cumulative effects may be more detectable than wave amplitude itself.

Abstract

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.