Gravitational waves from a spinning particle in circular orbits around a rotating black hole

TL;DR

This paper derives a post-Newtonian formula for gravitational wave energy flux from a spinning particle in circular orbit around a Kerr black hole, extending previous models to include particle spin effects.

Contribution

It introduces a new post-Newtonian expansion of gravitational wave luminosity that accounts for the linear order of particle spin in Kerr black hole backgrounds.

Findings

Derived the energy flux formula up to (v/c)^5 order including spin effects.

Extended the Teukolsky formalism to spinning particles using Papapetrou and Dixon equations.

Provided guidelines for future post-Newtonian modeling of spinning compact object inspirals.

Abstract

Using the Teukolsky and Sasaki-Nakamura formalisms for the perterbations around a Kerr black hole, we calculate the energy flux of gravitational waves induced by a {\it spinning} particle of mass $\mu$ and spin $S$ moving in circular orbits near the equatorial plain of a rotating black hole of mass $M (\gg \mu)$ and spin $Ma$. The calculations are performed by using the recently developed post-Newtonian expansion technique of the Teukolsky equation. To evaluate the source terms of perturbations caused by a {\it spinning} particle, we used the equations of motion of a spinning particle derived by Papapetrou and the energy momentum tensor of a spinning particle derived by Dixon. We present the post-Newtonian formula of the gravitational wave luminosity up to the order $(v/c)^5$ beyond the quadrupole formula including the linear order of particle spin. The results obtained in this paper will be an important guideline to the post-Newtonian calculation of the inspiral of two spinning compact objects.