Dynamics of Pressure-Free Matter in General Relativity

Abstract

An orthonormal tetrad system and associated coordinate system is obtained, which may be used to locally describe any dust-filled space-time. This is used to study dust-filled spaces in which there exist multiply transitive groups of motions; all such spaces are classified in detail. Spaces containing shear-free dust are also considered; it is shown that σ = 0 ⇒ ωΘ = 0. Three classes of solution with σ = 0, ω ≠ 0 are studied. Several new solutions of the field equations are contained in these results.