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We reformulate the theory of Schwarzschild black hole perturbations in termsof the metric perturbation in the Lorenz gauge. In this formulation, eachtensor-harmonic mode of the perturbation is constructed algebraically from 10scalar functions, satisfying a set of 10 wavelike equations, which aredecoupled at their principal parts. We solve these equations using numericalevolution in the time domain, for the case of a pointlike test particle set ina circular geodesic orbit around the black hole. Our code uses characteristiccoordinates, and incorporates a constraint damping scheme. Theaxially-symmetric, odd-parity modes of the perturbation are obtainedanalytically. The approach developed here is especially advantageous inapplications requiring knowledge of the local metric perturbation near a pointparticle; in particular, it offers a useful framework for calculations of thegravitational self force.Comment: 29 pages, 21 eps figure

Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation