Gravitation in a plane space. Equivalence principle for bulk bodies of electromagnetic structure

Abstract

In a previous paper [1] the author proposed a new linear nonmetric theory of gravitation in a plane space by giving the Einstein values for the four effects of the general theory of relativity (GTR). The field and motion equations were constructed on the basis of Lagrangians selected by the Hamilton principle. The gravitational field potential (GF) was a symmetric tensor of the second rank ψ_μν. A nonlinear extension of the theory is carried out in this paper on the basis of a single Lagrangian of the GF interaction with matter fψ_μν T^μν + λψT, where T^μν is the energy-momentum tensor of matter including the GF, f and λ are arbitrary constants of the theory. Within the framework of the nonlinear theory which yields the Einstein values for the four GTR effects, an additional condition is obtained which is imposed on the five arbitrary constants of the theory from which the satisfiability of the weak equivalence principle for bulk bodies of electromagnetic structure follows.