Algebraically general and gravito-electric rotating dust

Faculty of Applied Sciences TW16, Gent University, Galglaan 2, 9000 Gent, Belgium

Abstract

An invariant classification scheme of algebraically general rotating dust with a purely electric Weyl tensor is presented. It turns out that the vorticity vector of the dust congruence is necessarily parallel to a Weyl principal vector, which is moreover geodesic. An explicit metric expression can be obtained for the subclass of expanding models with one functionally independent zero-order Riemann invariant. The basic equations for the general case, where there are two such invariants, are given within a weighted 1+1+2 tetrad formalism.