Various problems of general relativity with and without a gravitational field

Abstract

A consistent principle of equivalence is formulated. An example of the necessity of strict observance of Einstein’s rule for the transformation of tensor coordinates is given. The problem of a homogeneous stationary gravitational field is being solved. All metrics with non-zero curvature. A metric for the space of constant curvature, different from the De Sitter space, is found. A stationary space with a cosmological redshift has been discovered, which creates the effect of accelerated expansion. It is shown that the plane-parallel motion of gas in a force field obeys the law of compression-expansion of the shock adiabat.