Einstein Tensor, Einstein-Hilbert Action and Generalizations

Abstract

Einstein tensor Tmv=Rmv-1/2Rgmv, m, v,= 1, 2, 3, 4, was mathematically generalized by two authors. V. M. Stanković [1, 2, 3], four kinds of generalized Einstein Tensor are defined. The results presented in the last section of master thesis [2] initiated this research. On the other hand, the family of Energy Momentum tensors with respect to generalized Riemannian spaces GR4 is presented in [5]. This paper is consisted of three sections. In the Section 1, which is introduction and motivation, basic terms for further presentation, Ricci identities, and their generalizations are presented. In Section 2, we review the results presented in [1, 2, 3, 4]. In Section3, which is the main part of this presentation, another way for working with Einstein tensor and some other terms which have been used in physics is presented. In this paper of presentation, the previous two geometrical approaches to physical terms are compared.