By Alexander Poltorak
Kuban University
Department of Theoretical Physics
Krasnodar / USSR

1980

Abstract

In the following GR9 Conference abstract we briefly considered a covariant reformulation of the GR from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a perspective of geometrodynamics, a definition of a reference frame as a differential manifold with an affine connection results in separation of the respective contributions of inertial and gravitational fields represented by the affine connection and the nonmetricity tensor within the Levi-Civita connection of GR. Resulting decomposition of Riemannian, Ricci and Einstein curvature tensors into affine and nonmetric parts allows recasting of Einstein’s field equations in a form invariant with respect to the choice of a reference frame, wherein the gravity is described by nonmetricity of space-time. A covariant Lagrangian is proposed leading to the same field equation. All three approaches ultimately lead to the same fully covariant theory of gravitation with a covariant tensor of energy-momentum of the gravitational field and differential and integral conservation laws. The role of reference frames, as distinguished from coordinate systems, is discussed.

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