Space tensors in general relativity II: Physical applications

Abstract

The general theory of space tensors is applied to the study of a space-time manifoldsV ₄ carrying a distinguished time-like congruence Γ. The problem is to determine a physically relevant spatial tensor analysis$\left( {\tilde \nabla ,\tilde \nabla _T } \right)$ over (V ₄, Γ), in order to proceed to a correct formulation of Relative Kinematics and Dynamics.

This is achieved by showing that each choice of$\left( {\tilde \nabla ,\tilde \nabla _T } \right)$ gives rise to a corresponding notion of ‘frame of reference’ associated with the congruence Γ. In particular, the frame of reference (Γ, ∇*) determined by the standard spatial tensor analysis$\left( {\tilde \nabla *,\tilde \nabla *_T } \right)$ is shown to provide the most natural generalization of the concept of frame of reference in Classical Physics.

The previous arguments are finally applied to the study of geodesic motion inV ₄. As a result, the general structure of the gravitational fields in the frame of reference (Γ, ∇*) is established.