The gravitational field of a point charge and finiteness of self-energy

Singularities in the metric of classical solutions of the Einstein equations (the Schwarzschild, Kerr, Reissner-Nordstroem, and Kerr-Newman solutions) give rise to generalized functions in the Einstein tensor. A technique based on the limiting sequence of solutions is used to analyze these functions, which can have a more complex behavior than the Dirac delta function. We show that the solutions will satisfy the Einstein equations everywhere if the energy-momentum tensor has an appropriate singular addition of nonelectromagnetic origin. When this addition term is included, the total energy turns out to be finite and equal to mc(2), while the angular momentum for the Kerr and Kerr-Newman solutions is mca. Since the Reissner-Nordstroem and Kerr-Newman solutions correspond to a point charge in classical electrodynamics, the result allows us to take a fresh look at the divergence of the self-energy of a point charge. (c) 2005 Pleiades Publishing, Inc.