

3 Post-Newtonian Expansion of the Regge-Wheeler
Equation
In this section, we review a post-Newtonian expansion method for
the Schwarzschild background, based on the Regge-Wheeler equation.
We focus on the gravitational waves emitted to infinity, but not on
those absorbed by the black hole. The black hole absorption is
deferred to Section 4, in which we review the
Mano-Suzuki-Takasugi method for solving the Teukolsky equation.
Since we are interested in the waves emitted to
infinity, as seen from Equation (26), what we need is a method to evaluate
the ingoing wave Teukolsky function
, or its counterpart in the
Regge-Wheeler equation,
, which are related by Equation (59). In addition, we assume
whenever it is
necessary throughout this section. Formulae and equations for
are obtained
from the symmetry
.

