GENERAL-RELATIVISTIC 1+3 ORTHONORMAL FRAME APPROACH

The dynamical equations of an extended 1 + 3 orthonormal frame approac h to the relativistic description of spacetime geometries are explicit ly presented and discussed in detail. In particular, the Bianchi ident ities for the Weyl curvature tensor occur in a fully expanded form, as they are given a central role in the extended formalism. It is shown how one can naturally introduce local coordinates, both in the 1 + 3 t hreading and the ADM 3 + 1 slicing context. By specializing the genera l 1 + 3 dynamical equations it is demonstrated how a number of problem s of interest can be obtained. In particular, the simplest choices of spatial frames for spatially homogeneous cosmological models, locally rotationally symmetric spacetime geometries, cosmological models with an Abelian isometry group G(2) and 'silent' dust cosmological models a re discussed.