Physics – Classical Physics
Scientific paper
Oct 1974
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974gregr...5..573m&link_type=abstract
General Relativity and Gravitation, Volume 5, Issue 5, pp.573-591
Physics
Classical Physics
10
Scientific paper
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 analysisleft( {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 ofleft( {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 analysisleft( {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.
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