Interior Schwarzschild Solutions and Interpretation of Source Terms
Abstract
The solutions of the Einstein field equations, previously used in deriving the selfenergy of a point charge, are shown to be nonsingular in a canonical frame, except at the position of the particle. A distribution of "dust" of finite extension is examined as the model whose limit is the point particle. The standard "proper restmass density" is related to the bare restmass density. The lack of singularity of the initial metric g_{μν} is in contrast to the Schwarzschild type singularity of standard coordinate systems. Our solutions for the extended source are nonstatic in general, corresponding to the fact that a charged dust is not generally in equilibrium. However, the solutions become static in the point limit for all values of the baresource parameters. Similarly, the selfstresses vanish for the point particle. Thus, a classical point electron is stable, the gravitational interaction cancelling the electrostatic selfforce, without the need for any extraneous "cohesive" forces.
 Publication:

Physical Review
 Pub Date:
 October 1960
 DOI:
 10.1103/PhysRev.120.321
 Bibcode:
 1960PhRv..120..321A