Relativity on 3-manifolds (Q1576189)

The paper describes how to translate the main spacetime notions and dynamics in a 3-dimensional setting. A pseudo-Riemannian manifold \((M^3,g)\) is endowed with a physical observer \(X\) (i.e. a nonsingular vector field with the norm bounded in \((1,0)\). The triple \((M^3, g, X)\) is a ``shadow'' of a spacetime if some specific tensorial equations on \(M^3\) are satisfied. Examples connected to the Schwarzschild and to the de Sitter solutions (as well as a new ``vacuum'' one) are given.