Theory of Gravity: a Classical Field Approach in Curved Space-Time

A new approach to the theory of gravity is proposed. A second-rank tensor field is chosen to be the potential of the gravitational field. The gravitational field is related to the metric tensor of space--time, and all phenomena occur in curved space--time. A variational principle is established, and the gravitational field equations are derived. The energy--momentum density tensor of the gravitational field and its conservation law are obtained. The source of the gravitational field is the energy--momentum density of all kinds of matter, including the gravitational field itself. A Lagrangian of the gravitational field is proposed that correctly describes local observable gravitational phenomena in the second-order approximation. The energy density of the gravitational field is positive. Estimates are obtained for the gravitational energy defect, the difference between the inertial and gravitational masses of a body, and the effect of the external gravitational field on the mass of a body. The new approach to the description of the gravitational field and its energy provides additional incentives search possibilities of experimental verification of the phenomena of gravitation in strong fields.