On finding fields and self-force in a gauge appropriate to separable wave equations II

Gravitational waves from the inspiral of a stellar-size black hole to a supermassive black hole can be accurately approximated by a point particle moving in a Kerr background. A procedure for finding the renormalized self-force from the Tuekolsky equation \footnote{Teukolsky, S. A., Astrophys. J., \textbf{185}, 635-647, (1973)} has been outlined in the separate talk and paper \footnote{T.~S.~Keidl, J.~L.~Friedman, A.~G.~Wiseman, Phys. Rev. D, in press; gr-qc0611072}. A singular metric has been computed in THZ coordinates \footnote{K.\ S.\ Thorne and J.\ B.\ Hartle, Phys. Rev. D {\bf 31}, 1815 (1985)} \footnote{X.-H.\ Zhang, Phys. Rev. D {\bf 34}, 991 (1986)} (locally inertial on a geodesic), and has a simple form. In this talk, we focus on carrying out the procedure using the lowest order piece of the singular metric in Schwarzschild coordinates. We compute a lowest order non-singular $\psi_0$ and analyze the non-singular metric that arises.