Extended bodies with spin induced quadrupoles on circular equatorial orbits in Kerr spacetime

TL;DR

This paper analyzes the motion of spinning extended bodies with spin-induced quadrupoles in Kerr spacetime, deriving orbit frequencies and relations under different spin supplementary conditions.

Contribution

It provides new calculations of orbit frequencies and explicit relations for bodies with spin-induced quadrupoles in Kerr spacetime, considering different SSCs.

Findings

Orbit frequencies for spin-induced quadrupoles in Kerr

Explicit four-velocity and four-momentum relations

Comparison of SSC effects on motion

Abstract

This work discusses the motion of extended test bodies as described by the Mathisson-Papapetrou-Dixon (MPD) equations in the pole-dipole-quadrupole approximation. We focus on the case that the quadrupole is solely induced by the spin of the body which is assumed to move on a circular equatorial orbit in a Kerr background. To fix the center of mass of the MPD body we use two different spin supplementary conditions (SSCs): the Tulczyjew-Dixon SSC and the Mathisson-Pirani SSC. We provide the frequencies of the circular equatorial orbits for the pole-dipole-(spin induced) quadrupole approximation of the body for both SSCs. In the process we develop an explicit four-velocity four-momentum relation for a pole-dipole-quadrupole body under the Mathisson-Pirani SSC.