Finding Fields and Self-Force in a Gauge Appropriate to Separable Wave Equations

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 paper \footnote{T.~S.~Keidl, J.~L.~Friedman, A.~G.~Wiseman, Phys. Rev. D, in press; gr-qc0611072}. This talk focuses on analytic work developed in this formalism and incorporating the $l=0$ and $l=1$ parts of the self-force. The self-force is calculated from either the renormalized spin $+2$ or the spin $-2$ Weyl scalar ($\psi_0$ or $\psi_4$). The self-force is can then be calculated algebraically from either renormalized Weyl scalar.