

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 [57, 60]. 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 quadrapole
formula. We can find that our result agrees with the standard
post-Newtonian results up to
[8] in the limit
.

