

5.3 Slightly eccentric orbit around a
Schwarzschild black hole
Next, we consider a particle in slightly eccentric orbit on the
equatorial plane around a Schwarzschild black hole (see [34],
Section 7). We define
as the minimum of the radial potential
. We also define
an eccentricity parameter
from the maximum radius of the orbit
, which is given by
. These conditions are explicitly given by
We assume
.
In this case,
is given to
by
where
is the orbital angular frequency in the circular
orbit case. We now present the energy and angular momentum
luminosity, accurate to
and to
beyond Newtonian order. They are given by
and
where
is
the Newtonian angular momentum flux expressed in terms of
,
and the
-independent terms in both
and
are the
same and are given by the terms in the case of circular orbit,
Equation (174).

