The principle of least action in covariant theory of gravitation

Abstract

The integral equations for calculation of metric, equations of substance motion, as well as equations for gravitational and electromagnetic fields in covariant theory of gravitation are obtained by means of variation of action functional. In covariant form stress-energy tensor of gravitational field, strength tensor of gravitational field and 4-current of mass are determined. The meaning of the cosmological constant and its relation to the components of energy density in action functional are explained. The results obtained prove the validity of Mach's principle, assuming that gravitation effects are due to the flows of gravitons. The idea that metric can be entirely determined by variables describing fields’ properties is substantiated.