Generalized frames of references and intrinsic Cauchy problem in General Relativity

Abstract

Starting from an ordinary frame of reference in General Relativity, and its anholonomic structure, we consider a review of more general quasi-product structure, in a differentiable (or riemannian) manifold, that can be deal with the same anholonomic techniques. The general case contains, in particular, the generalization of ordinary frame of reference, in the sense of polar continua, with one scalar supplementary field (non-orthogonal 1 x 3 structure). Finally, the anholonomic formalism is developed for the intrinsic Cauchy problem in General Relativity (gravitational equations), in the case of non polar continua; properly spatial variables are the following: metric _γik , vector potential γi, deformation rate ${{\tilde{K}}_{{ik}}}$ pure mass density µ ₀ , heat flux ${{\tilde{Q}}_{i}}$ and temperature T.