Dixon's extended bodies and weak gravitational waves

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.

12 pages, Latex svjour2.cls article class, no figures. Note that the second term in the rhs of Eq. (2) was misprinted in the published version of the paper [General Relativity and Gravitation, Vol. 41, 105 (2008)]. The results are but correct

References in corpus (1)

• Quadrupole effects on the motion of extended bodies in Schwarzschild spacetime

Cited by in corpus (7)

• Dynamics of quadrupolar bodies in a Schwarzschild spacetime
• Deviation and precession effects in the field of a weak gravitational wave
• Covariant Equations of Motion of Extended Bodies with Arbitrary Mass and Spin Multipoles
• The Distributional Stress-Energy Quadrupole
• Covariant Equations of Motion Beyond the Spin-Dipole Particle Approximation
• Influence of gravitational waves upon light in the Minkowski background: from null geodesics to interferometry
• Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations