Construction and invariant classification of perfect fluids in general relativity

Abstract

A formalism for classifying and constructing perfect fluids is developed. The Ricci tensor and its first covariant derivatives in a comoving frame are expressed as functions of energy density, pressure, their gradients and the kinematic quantities. All conformally flat perfect fluids are constructed and thus also classified. In general the third covariant derivative is needed for a complete classification of these metrics.