

5 Gravitational Waves from a Particle Orbiting a
Black Hole
Based on the ingoing wave functions discussed in Section 3 and 4, we can derive the
gravitational wave energy and angular momentum flux emitted to
infinity. The formula for the energy and the angular momentum
luminosity to infinity are given by Equations (48) and (49). Since most of the calculations are
very long, we show only the final results. In [34
], some details of the
calculations are summarized. We define the post-Newtonian expansion
parameter by
, where
is the mass of the black hole and
is the orbital
angular frequency of the particle. Since the parameter
is directly related
to the observable frequency, this result can be compared with the
results by another method easily.

