Rotating perfect fluid models in general relativity

Abstract

AbstractThe 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 ansätze, and (ii) the angular behaviour is a valuable commodity. This latter observation follows 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, approximation schemes based on a series expansion in the angular velocity are suggested. A pioneering work, due to Hartle, explores the global properties of matched space‐times to quadratic order in the angular velocity.As a first example of the applications, it is shown that the rigidly rotating incompressible fluid cannot be Petrov type D.