A differential form approach for rotating perfect fluids in general relativity

Abstract

A compact formulation for general relativistic, axisymmetric perfect fluids in stationary rotation is introduced; the case of differential rotation is included. The basic variables are differential 1-forms with immediate physical relevance. As an illustration of the method, the authors give the derivation of an irrotational solution found recently. With the matching problem in mind, stationary, axially symmetric vacuum fields are considered as formal perfect fluids; it is shown that they can always be brought to a 'rigid rotation' or to an 'irrotational' form. Two discrete transformations (reminiscent of the Kramer-Neugebauer transformation) that may be useful for solution-generating purposes are introduced. A formulation of the Ernst type is given for the 'irrotational' vacuum case.