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Interior Schwarzschild Solutions and Interpretation of Source Terms

1960; American Institute of Physics; Volume: 120; Issue: 1 Linguagem: Inglês

10.1103/physrev.120.321

1536-6065

R. Arnowitt, S. Deser, Charles W. Misner,

Biofield Effects and Biophysics

The solutions of the Einstein field equations, previously used in deriving the self-energy 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 rest-mass density" is related to the bare rest-mass density. The lack of singularity of the initial metric ${g}_{\ensuremath{\mu}\ensuremath{\nu}}$ 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 bare-source parameters. Similarly, the self-stresses vanish for the point particle. Thus, a classical point electron is stable, the gravitational interaction cancelling the electrostatic self-force, without the need for any extraneous "cohesive" forces.