New Equations for Gravitation with Riemann Tensor and 4-Index Energy-Momentum Tensors for Gravitation and Matter

Abstract

A generalized version of the Einstein equations in the 4-index form, containing the Riemann tensor linearly, is derived. It is shown, that the gravitational energy-momentum density tensor outside a source is represented across the Weyl tensor vanishing at the 2-index contraction. The 4-index energy-momentum density tensor for matter also is constructed.Comment: Published in: "Z.Zakir (2003) Structure of Space-Time and Matter. CTPA, Tashkent