Properties of the invariant components of the Weyl tensor implied by the Bianchi identities

Abstract

For vacuum regions in pseudo-Riemannian spaces in finite or infinitely large volumes of four-dimensional spaces, the Riemann tensor becomes the Weyl tensor. Based on the conditions of continuity for the space geometry, the form of the invariant components of the Weyl tensor, as functions of the coordinate arguments in the Fermi variables on canonical global time coordinate curves, is determined. With reference to a complete system of independent canonical invariants of the different types of Weyl tensor in four-dimensional spaces, the conditions of continuity are used to determine the form of these invariants as functions of the comoving individual Fermi coordinates at points of the pseudo-Riemannian spaces.