Gravitational radiation from a particle in circular orbit around a black hole. IV. Analytical results for the slowly rotating case

A particle of mass $\mu$ moves on a circular, equatorial orbit around a slowly rotating black hole of mass $M$. If $\mu \ll M$, the gravitational waves emitted by the particle can be computed using the Teukolsky perturbation formalism. If, further, the orbital frequency $\Omega$ is such that $v\equiv {\left(M\Omega \right)}^{\frac{1}{3}}$ is small, then the Teukolsky equation can be integrated analytically. I present such calculations here, and derive corrections to the gravitational waveforms and luminosity due to the slow rotation of the black hole. The results are in agreement with a more general analysis, based on post-Newtonian theory, by Kidder, Will, and Wiseman.