Post-Newtonian expansion of gravitational waves from a compact star orbiting a rotating black hole in Brans-Dicke theory: Circular orbit case

Abstract

In the context of Brans-Dicke theory, we calculate the post-Newtonian expansion of the scalar part of gravitational radiation from a compact star in a circular orbit around a rotating black hole up to O(ν5) beyond the leading, Newtonian-dipole formula. The calculation is based on a method developed recently by Sasaki in the Schwarzschild case in the context of general relativity. The orbit of a compact star is restricted on the equatorial plane. Then we estimate the post-Newtonian effect of scalar radiation to the orbital evolution of coalescing compact binaries. We find that the post-Newtonian effect of scalar radiation is small in the LIGO band if we take into account the experimental bound of the Brans-Dicke parameter ωBD>500. On the other hand, we find that the post-Newtonian effect of the scalar radiation is not negligible for the LISA experiment.