Quadrupole effects on the motion of extended bodies in Schwarzschild spacetime

TL;DR

This paper investigates how quadrupole moments influence the motion of extended bodies in Schwarzschild spacetime, revealing measurable deviations from geodesic paths without affecting the clock effect.

Contribution

It extends Dixon's model to include quadrupolar effects and analyzes their impact on body motion in Schwarzschild spacetime under specific restrictions.

Findings

Quadrupole moments cause measurable deviations from geodesic motion.

The standard clock-effect remains unaffected by quadrupolar structure.

Internal structure influences orbital dynamics without altering certain relativistic effects.

Abstract

The motion of an extended body up to the quadrupolar structure is studied in the Schwarzschild background following Dixon's model and within certain restrictions (constant frame components for the spin and the quadrupole tensor, center of mass moving along a circular orbit, etc.). We find a number of interesting situations in which deviations from the geodesic motion, due to the internal structure of the particle, can originate measurable effects. However, the standard clock-effect for a pair co/counter-rotating bodies spinning up/down is not modified by the quadrupolar structure of the particle.