Comoving and inertial frames of reference

Abstract

The possibility of constructing the non-linear equations of the general 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-dimensional absolute acceleration relative to a family of inertial geodesies, which satisfy the field equations in their orbits. Unless the law of universal gravitation is explicitly taken into account, the equations of the GTR and the field equations do not constitute closed systems. The law of universal gravitation imposes additional restrictions on the gravitational field and the trajectories of free particles. The description of the relativistic gravitational fields and the free motion of mass particles is based on using both the thermodynamic energy scalar mc 2 and the potential energy scalar mU of the particles, just as in Newtonian mechanics or in Minkowski space in the special theory of relativity (STR). In a comoving frame of reference the scalar U satisfies a three-dimensional Poisson equation. In the light of the theory proposed here, many well-known solutions of the GTR have to be reinterpreted.