On Spacetimes Admitting Shear-free, Irrotational, Geodesic Timelike Congruences

TL;DR

This paper provides a detailed analysis of general relativistic spacetimes with shear-free, irrotational, geodesic timelike congruences, exploring various energy-momentum configurations and their implications for cosmological models.

Contribution

It systematically classifies and examines spacetimes with specific congruence properties, including various physically relevant energy-momentum tensors and special cases like perfect fluids and magnetic fields.

Findings

Friedmann-Robertson-Walker models are included.

Models with anisotropic and viscous fluids are analyzed.

Conditions for tilting perfect fluids are discussed.

Abstract

A comprehensive analysis of general relativistic spacetimes which admit a shear-free, irrotational and geodesic timelike congruence is presented. The equations governing the models for a general energy-momentum tensor are written down. Coordinates in which the metric of such spacetimes takes on a simplified form are established. The general subcases of `zero anisotropic stress', `zero heat flux vector' and `two component fluids' are investigated. In particular, perfect fluid Friedmann-Robertson-Walker models and spatially homogeneous models are discussed. Models with a variety of physically relevant energy-momentum tensors are considered. Anisotropic fluid models and viscous fluid models with heat conduction are examined. Also, models with a perfect fluid plus a magnetic field or with pure radiation, and models with two non-collinear perfect fluids (satisfying a variety of physical conditions) are investigated. In particular, models with a (single) perfect fluid which is tilting with respect to the shear-free, vorticity-free and acceleration-free timelike congruence are discussed.