EINSTEIN'S THEORY OF GRAVITATION AS A LAGRANGIAN THEORY FOR TENSOR FIELDS

Abstract

Einstein's theory of gravitation (ETG) is considered as a Lagrangian theory of tensor fields over (pseudo) Riemannian spaces without torsion (Vn spaces, n=4) by means of the method of Lagrangians with covariant derivarives (MLCD). In a trivial manner Euler–Lagrange's equations as Einstein's equations are obtained. The corresponding energy–momentum tensors (EMT's) are found for the standard for the ETG Lagrangian invariant on the basis of the covariant Noether identities. The symmetric energy–momentum tensor of Hilbert appears as an element irrelevant to the whole scheme of the considered Lagrangian thoery of tensor fields over Vn spaces despite of the fact that it has some elements of the structure of the variational EMT of Euler–Lagrange. The notion of the active gravitational rest mast density is related to the variational EMT of Euler–Lagrange and on this basis to a certain extent to the EMT of Hilbert.