

5.2 Circular orbit on the equatorial plane around
a Kerr black hole
Next, we consider a particle in a circular orbit on the equatorial
plane around a Kerr black hole [58]. In this case,
the orbital angular frequency
is given by
where
is the
orbital angular frequency of the circular orbit in the
Schwarzschild case,
,
, and
is the orbital radius in the
Boyer-Lindquist coordinate. The effect of the angular momentum of
the black hole is given by the corrections depending on the
parameter
. Here,
is arbitrary as
long as
. The luminosity is given up to
(4PN order) by

