### 5.1 Circular orbit around a Schwarzschild black hole

First, we present the gravitational wave luminosity for a particle in a circular orbit around a
Schwarzschild black hole [100, 105]. In this case, is given by , where is
the orbital radius, in standard Schwarzschild coordinates. The luminosity to is given by
where is the Newtonian quadrupole luminosity given by
This is the 5.5PN formula beyond the lowest, Newtonian quadrupole formula. We can find that our
result agrees with the standard post-Newtonian results up to [13] in the limit
.