  We reformulate the theory of Schwarzschild black hole perturbations in terms
of the metric perturbation in the Lorenz gauge. In this formulation, each
tensor-harmonic mode of the perturbation is constructed algebraically from 10
scalar functions, satisfying a set of 10 wavelike equations, which are
decoupled at their principal parts. We solve these equations using numerical
evolution in the time domain, for the case of a pointlike test particle set in
a circular geodesic orbit around the black hole. Our code uses characteristic
coordinates, and incorporates a constraint damping scheme. The
axially-symmetric, odd-parity modes of the perturbation are obtained
analytically. The approach developed here is especially advantageous in
applications requiring knowledge of the local metric perturbation near a point
particle; in particular, it offers a useful framework for calculations of the
gravitational self force.
