A Metric Theory of Gravitation without Minimal Coupling of Matter and Gravitational Field

A metric theory of gravitation is suggested which reduces to Einstein's theory in the case of vanishing matter. If matter is present, in the Lagrangian formulation of the theory the principle of minimal coupling is given up by directly linking the matter variables to the curvature tensor. The theory contains a free parameter of dimension length. It is considered not to be a universal constant but a length characteristic for the mass of the material system described. Results diverging from those of General Relativity are to be expected for regions with high curvature i. e. especially for gravitational collapse and dense phases of the cosmos. An exact, static and spherically symmetric solution with constant matter density is discussed; it indicates that, possibly, gravitational collapse is avoided.