Towards a Covariant Theory of Gravitation

In the following GR9 (1980) 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 Published in Abstracts of Contributed Papers for the 9th International Conference on General Relativity and Gravitation, Jena, GDR, 1980 (This rendition of the paper is an improved English translation from the Russian original and varies slightly from the published paper.) Current address: General Patent Corporation, Montebello Park, 75 Montebello Road, Suffern, NY 10901-3740 USA. E-mail: [email protected].