Interior Schwarzschild Solutions and Interpretation of Source Terms

R. Arnowitt, S. Deser, and C. W. Misner
Phys. Rev. 120, 321 – Published 1 October 1960
PDFExport Citation

Abstract

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 gμν 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.

  • Received 27 April 1960

DOI:https://doi.org/10.1103/PhysRev.120.321

©1960 American Physical Society

Authors & Affiliations

R. Arnowitt*,†, S. Deser*, and C. W. Misner

  • Department of Physics, Brandeis University, Waltham, Massachusetts

  • *Supported in part by the National Science Foundation and by the Air Force Office of Scientific Research under Contract.
  • On leave from Department of Physics, Syracuse University, Syracuse, New York.
  • Alfred P. Sloan Research Fellow. On leave from Palmer Physical Laboratory, Princeton University, Princeton, New Jersey.

References (Subscription Required)

Click to Expand
Issue

Vol. 120, Iss. 1 — October 1960

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Journals Archive

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×