Space tensors in general relativity I: Spatial tensor algebra and analysis

Details Space tensors in general relativity I: Spatial tensor algebra and analysis Space tensors in general relativity I: Spatial tensor algebra and analysis

Oct 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974gregr...5..555m&link_type=abstract

General Relativity and Gravitation, Volume 5, Issue 5, pp.555-572

Mathematics

12

Scientific paper

A pair (M, Γ) is defined as a Riemannian manifold M of normal hyperbolic type carrying a distinguished time-like congruence Γ. The spatial tensor algebra D associated with the pair (M, Γ) is discussed. A general definition of the concept of spatial tensor analysis over (M, Γ) is then proposed. Basically, this includes a spatial covariant differentiationtilde nabla and a time-derivativetilde nabla _T , both acting on D and commuting with the process of raising and lowering the tensor indices. The torsion tensor fields of the pairleft( {tilde nabla ,tilde nabla _T } right) are discussed, as well as the corresponding structural equations. The existence of a distinguished spatial tensor analysis over (M, Γ) is finally established, and the resulting mathematical structure is examined in detail.

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