

5.4 Slightly eccentric orbit around a Kerr black
hole
Next, we consider a particle in a slightly eccentric orbit on the
equatorial plane around a Kerr black hole [53]. We define
the orbital radius
and the eccentricity in the same way as in the
Schwarzschild case by
We also assume
. In this case,
is given to
by
We now give the energy and angular momentum
luminosity that are accurate to
and to
beyond Newtonian order:

