COMOVING AND INERTIAL FRAMES OF REFERENCE

The possibility of constructing the non-linear equations of the genera l theory of relativity (GTR) incorporating a potential energy concept is demonstrated. Solutions of the generalized equations are considered for the motions of individual particles with non-vanishing four-dimen sional absolute acceleration relative to a family of inertial geodesic s, which satisfy the field equations in their orbits. Unless the law o f universal gravitation is explicitly taken into account, the equation s of the GTR and the field equations do not constitute closed systems. The law of universal gravitation imposes additional restrictions on t he gravitational field and the trajectories of free particles. The des cription of the relativistic gravitational fields and the free motion of mass particles is based on using both the thermodynamic energy scal ar mc2 and the potential energy scalar mU of the particles, just as in Newtonian mechanics or in Minkowski space in the special theory of re lativity (STR). In a comoving frame of reference the scalar U satisfie s a three-dimensional Poisson equation. In the light of the theory pro posed here, many well-known solutions of the GTR have to be reinterpre ted.