The energy tensor of matter in the projectve theory of relativity

Abstract

In the projective theory of relativity the 5-dimensional field equation $$_{\mu \nu } $$ and the resulting equation of motion Tμυ;μ = 0 are investigated. There Tμυ stands for the 5-dimensional tensor of macroscopic matter. The 4-dimensional field equations and equation of motion obtained by projection are a generalization of Einstein's theory of general relativity and Maxwell's electrodynamics, involving a scalar field φ.They contain a single constant φ0.The weak field approximation is investigated for the case of an ideal fluid and leads to Newton's mechanics, including Newton's gravitational law, and to Maxwell's electrodynamics. For the constant φ0 one obtains the approximate value φ0c4/γN with Newton's gravitational constant γN.For homogeneous and isotropic cosmological models consisting of matter only the general solution for the radius K of curvature is given. This solution is independent of the equation of state of matter For a pure dust universe the general solution for the scalar field φ is given. For a closed universe a power law φ ∿K−1 is valid which leads to Mach's principle. The calculation of the age of a closed universe yields over 7×109y,if one uses mean values of the present cosmological data.