ON SPACETIMES ADMITTING SHEAR-FREE, IRROTATIONAL, GEODESIC TIME-LIKE CONGRUENCES

A comprehensive analysis of general relativistic spacetimes which admi t a shear-free, irrotational and geodesic time-like congruence is pres ented. The equations governing the models for a general energy-momentu m tensor are written down. Coordinates in which the metric of such spa cetimes takes on a simplified form are established. The general subcas es of 'zero anisotropic stress', 'zero heat-flux vector' and 'two-comp onent fluids' are investigated. In particular, perfect-fluid Friedmann -Robertson-Walker models and spatially homogeneous models are discusse d. Models with a variety of physically relevant energy-momentum tensor s are considered. Anisotropic fluid models and viscous fluid models wi th heat conduction are examined. Also, models with a perfect fluid plu s a magnetic field or with pure radiation, and models with two non-col linear perfect fluids (satisfying a variety of physical conditions) ar e investigated. In particular, models with a (single) perfect fluid wh ich is tilting with respect to the shear-free, vorticity-free and acce leration-free time-like congruence are discussed.