On the formulation of Einstein general relativity in a phisycal reference system

Abstract

The research deals with the breaking of the evolution problem of a reversible material system in two different problems, the initial data problem and the restricted evolution problem. This breaking, intrinsically formulated, permits to study of the evolution of a perfect fluid which produces a spherically symmetric 4--manifold. By using different systems of coordinates adapted to the world-lines of this fluid, such as curvature coordinates, gaussian coordinates, gaussian polar coordinates and harmonic coordinates, different exact solutions are obtained. In particular, in gaussian coordinates, I have obtained two solutions already deduced, in a different way, by Wesson and Gutman, showing that they are physically equivalent. In addition, by considering the frames of reference associated to isotropic coordinates and spherical symmetry, I have obtained that the restricted evolution problem gives dynamic models non different from Einstein--deSitter or Friedman--Robertson--Walker or Wyman models; moreover, if the distribution of the fluid is initially regular in the symmetry center, and the Hubble parameter is constant, all the configurations of the fluid are demonstrated to be Euclidean hypersurfaces. Finally, I have studied the geometrical and physical characteristics of the class of reference frames associated to harmonic coordinates. Precisely, I express in relative form the harmonicity conditions and consider the so called “spatially harmonicity" of a reference frame in spherical symmetry. The initial data problem is then analyzed in polar coordinates and the obtained results are applied to special cases of exact solutions. [edited by author]