  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. This paper presents progress on finding the
electromagnetic and gravitational field of a point particle in a black-hole
spacetime and on computing the self-force in a ``radiation gauge.'' The gauge
is chosen to allow one to compute the perturbed metric from a gauge-invariant
component $\psi_0$ (or $\psi_4$) of the Weyl tensor and follows earlier work by
Chrzanowski and Cohen and Kegeles (we correct a minor, but propagating, error
in the Cohen-Kegeles formalism). The electromagnetic field tensor and vector
potential of a static point charge and the perturbed gravitational field of a
static point mass in a Schwarzschild geometry are found, surprisingly, to have
closed-form expressions. The gravitational field of a static point charge in
the Schwarzschild background must have a strut, but $\psi_0$ and $\psi_4$ are
smooth except at the particle, and one can find local radiation gauges for
which the corresponding spin $\pm 2$ parts of the perturbed metric are smooth.
Finally a method for finding the renormalized self-force from the Teukolsky
equation is presented. The method is related to the Mino, Sasaki, Tanaka and
Quinn and Wald (MiSaTaQuWa) renormalization and to the Detweiler-Whiting
construction of the singular field. It relies on the fact that the renormalized
$\psi_0$ (or $\psi_4$) is a {\em sourcefree} solution to the Teukolsky
equation; and one can therefore reconstruct a nonsingular renormalized metric
in a radiation gauge.
