TITLE:
On the Field Equations of General Relativity
AUTHORS:
Vu B. Ho
KEYWORDS:
General Relativity, Classical Field Equations, Riemann Curvature Tensor
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.1,
January
13,
2022
ABSTRACT: In this work, we examine the geometric character of the field equations of general relativity and propose to formulate relativistic field equations in terms of the Riemann curvature tensor. The resulted relativistic field equations are also integrated into the general framework that we have presented in our previous works that all known classical fields can be expressed in the same dynamical form. We also discuss a possibility to reformulate the field equations of general relativity so that the Ricci curvature tensor and the energy-momentum tensor can appear symmetrically in the field equations without violating the conservation law stated by the covariant derivative.