Rotating perfect fluid models in general relativity

The various schemes for studying rigidly rotating perfect fluids in general relativity are reviewed. General conclusions one may draw from these are: (i) There is a need to restrict the scope of the possible ansatze, and (ii) the angular behaviour is a valuable commodity. This latter observation fol lows from a large number of analytic models exhibiting a NUT-like behaviour . A method of getting around problem (ii) is presented on a simple example. To alleviate problem (i) for rigidly rotating perfect fluids, approximatio n schemes based on a series expansion in the angular velocity are suggested . A pioneering work, due to Hartle, explores the global properties of match ed space-times to quadratic order in the angular velocity. As a first example of the applications, it is shown that the rigidly rotati ng incompressible fluid cannot be Petrov type D.