New version of the general theory of relativity (Initial principles. New gravitational field equation. New solutions)

Preprint (PDF Available) · February 2018with 1,687 Reads
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Abstract
There was obtained the general form of a gravity field metric tensor. With aid of the correspondence principle, this allows finding the simplest generally covariant equation of gravity field in isotropic space. The general relativity theory new version corresponds in full to the principles of Einstein’s gravity theory stated in 1913. One of spherically symmetric solutions of field equation corresponds to Schwarzschild solution, while most part of its Christoffel symbols are asymptotically equal to Christoffel symbols of Schwarzschild’s metric tensor. In particular, the gravity field acceleration given by the new solution coincides with the gravity field acceleration given by the Schwarzschild solution in weak fields. For homogeneous space, the field equation returns the metric with exponential dependence on time, which scale is imposed by space. Einstein’s equation in the new version performs another function: it allows calculating the full tensor of energy-momentum of matter and field via a metric tensor. Namely the new solution with the spherical symmetry in space without matter is the field of “gravity” forces oriented outwards. In this case, a role of “dark energy” is played by the gravity field negative energy density. Sizes of this object are proportional to absolute value of field energy and not limited at all. It is assumed that namely such solutions are responsible for the large-scale structure of the Universe. Key words: Einstein’s equation, homogeneous field, general relativity theory, gravity field equation, exact solutions, spherically symmetric fields, tensor of field energy-momentum, Universe’s non-uniformity, dark energy.
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