On test particles in general relativity

The field-to-particle approach is generalized to include the self-gravity of a test particle. The quantity which is identified as the four-momentum of the particle is found, for a charged particle, to be related to the Lorentz force, and, for a suitably defined free, spherically symmetric particle, to be the product of the particle's four-velocity and a constant scalar. In the latter case, the particle's world-line is a geodesic. In the Newtonian approximation, the apparent mass is the usual combination of proper mass and binding energy. The principal assumption is that the particle is small compared with variations in the background metric. Except for this constraint, both the background metric and the particle's internal structure (including gravity) are arbitrary.