### 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 [101]. 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
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