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

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.