On the $$(1+3)$$ ( 1 + 3 ) Threading of Spacetime

Abstract

We develop a (1 + 3) threading formalism of the spacetime with respect to a non-normalized timelike vector field. It is worth mentioning that in our approach the spatial distribution is not necessarily integrable. Thus, this formalism is suitable for general Lorentz metrics from both the theory of black holes and perturbation theory. Also, the simple form of the (1 + 3) decomposition of Einstein Field Equations stated in the paper, might have an important impact on the work of discovering new inhomogeneous cosmological models.