Dynamics of quadrupolar bodies in a Schwarzschild spacetime

TL;DR

This paper studies the motion of extended quadrupolar bodies in Schwarzschild spacetime, revealing how quadrupole moments influence dynamics and can generate spin angular momentum.

Contribution

It extends previous models by including quadrupole moments in the analysis of body dynamics in Schwarzschild spacetime, both numerically and analytically.

Findings

Quadrupole moments significantly affect the body's motion.

Presence of quadrupole can induce non-zero spin angular momentum.

Results differ from spin-only models, showing new dynamical behaviors.

Abstract

The dynamics of extended bodies endowed with multipolar structure up to the mass quadrupole moment is investigated in the Schwarzschild background according to the Dixon's model, extending previous works. The whole set of evolution equations is numerically integrated under the simplifying assumptions of constant frame components of the quadrupole tensor and that the motion of the center of mass be confined on the equatorial plane, the spin vector being orthogonal to it. The equations of motion are also solved analytically in the limit of small values of the characteristic length scales associated with the spin and quadrupole with respect to the background curvature characteristic length. The results are qualitatively and quantitatively different from previous analyses involving only spin structures. In particular, the presence of the quadrupole turns out to be responsible for the onset of a non-zero spin angular momentum, even if initially absent.