Authors: Ll. Bel
The Postulate of General covariance, a last choice that Einstein introduced in his General relativity theory of gravitation, endows the theory with an excessive generality that needs to be restrained. Otherwise it is easy to check that, beyond the first order of approximation, several space-time models, all of them derived from the original Schwarzschild's initial solution of Einstein's field equations corresponding to a static spherical source, would predict different results to two fundamental experiments: the measure of the force acting on a given passive test mass at a distance $R$ of the center of the source, or equivalently, its initial acceleration when falling from rest, and the comparison of two way transit times of light traveling into an optic fiber along a vertical direction and along a meridian. The last section describes how to find numeric, static and spherically symmetric, interior models with pre-selected mass $m$ and radius $R$ with $m/R<1$ or $m/R>1$ solving the horizon problem.
Comments: 12 Pages. Errata and minor errors correctrd
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