Dynamics of extended bodies with spin-induced quadrupole in Kerr spacetime: generic orbits

TL;DR

This paper investigates the motion of extended bodies with spin-induced quadrupoles in Kerr spacetime, revealing their effects on orbital dynamics and gravitational wave signals, with implications for astrophysical observations.

Contribution

It provides a detailed analysis of how quadrupole moments influence the motion of bodies in Kerr spacetime, including numerical simulations and implications for gravitational wave detection.

Findings

Quadrupole effects are negligible in extreme-mass-ratio inspirals for gravitational wave detectors.

No chaotic orbits found for physically realistic spins and quadrupoles.

Quadrupole moments significantly affect orbital motion and dynamics.

Abstract

We discuss motions of extended bodies in Kerr spacetime by using Mathisson-Papapetrou-Dixon equations. We firstly solve the conditions for circular orbits, and calculate the orbital frequency shift due to the mass quadrupoles. The results show that we need not consider the spin-induced quadrupoles in extreme-mass-ratio inspirals for spatial gravitational wave detectors. We quantitatively investigate the temporal variation of rotational velocity of the extended body due to the coupling of quadrupole and background gravitational field. For generic orbits, we numerically integrate the Mathisson-Papapetrou-Dixon equations for evolving the motion of an extended body orbiting a Kerr black hole. By comparing with the monopole-dipole approximation, we reveal the influences of quadrupole moments of extended bodies on the orbital motion and chaotic dynamics of extreme-mass-ratio systems. We do not find any chaotic orbits for the extended bodies with physical spins and spin-induced quadrupoles. Possible implications for gravitational wave detection and pulsar timing observation are outlined.