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

Abstract

Using the Teukolsky and Sasaki-Nakamura formalisms for the perturbations around a Kerr black hole, we calculate the energy flux of gravitational waves induced by a spinning particle of mass $\ensuremath{\mu}$ and spin $S$ moving in circular orbits near the equatorial plain of a rotating black hole of mass $M(\ensuremath{\gg}\ensuremath{\mu})$ and spin $\mathrm{Ma}$. 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 spinning particle, we use 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 ${(\frac{v}{c})}^{5}$ 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.