2004/12/30 by Plamen Fiziev
Physics and Astronomy · #gr-qc
published as in Proceedings of the Conference Contemporary Aspects of Astronomy, Theoretical and Gravitational Physics, May 20-22, 2004, Sofia, Bulgaria · 12 pages, latex file, no figures
arxiv created 2004/12/30 · arxiv updated 2009/12/01
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist a two-parameters family of such solutions to the Einstein equations which are physically distinguishable but only some of them describe the gravitational field of a single massive point particle with nonzero bare mass M0. In particular, the widespread Hilbert's form of Schwarzschild solution, which depends only on the Keplerian mass M<M0, does not solve the Einstein equations with a massive point particle's stress-energy tensor as a source. Novel normal coordinates for the field and a new physical class of gauges are proposed, in this way achieving a correct description of a point mass source in GR. We also introduce a gravitational mass defect of a point particle and determine the dependence of the solutions on this mass defect. The result can be described as a change of the Newton potential ϕ_N=-G_NM/r to a modified one: ϕ_G=-G_NM/ (r+G_N M/c2lnM0\over M) and a corresponding modification of the four-interval. In addition we give invariant characteristics of the physically and geometrically different classes of spherically symmetric static space-times created by one point mass. These space-times are analytic manifolds with a definite singularity at the place of the matter particle.