  Covariant structure of the self-force of a particle in a general curved
background has been made clear in the cases of scalar [Quinn], electromagnetic
[DeWittBrehme], and gravitational charges [QuinnWald]. Namely, what we need is
the part of the self-field that is non-vanishing off and within the past
light-cone of particle's location, the so-called tail. The radiation reaction
force in the absence of external fields is entirely contained in the tail. In
this paper, we develop mathematical tools for the regularization and propose a
practical method to calculate the self-force of a particle orbiting a
Schwarzschild black hole.
