Motivated by various space-time decomposition techniques in general relativity, a general framework of n + 1 decomposition is worked out, and its relation to earlier works is investigated. Orthogonal tensors are defined, based on a preferred vector field and one-form field. In contrast to earlier papers, neither a metric nor an (n + 1)-dimensional connection is used in the definition of n-dimensional derivatives. Equations corresponding to the Ricci and Bianchi identities are derived. A straightforward method is given to construct a unique (n + 1)-dimensional derivation from any n-dimensional derivative operator. Relations between the n- and (n + 1)-dimensional torsions and curvatures are derived.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics