The Slow-Rotation Approximation as a Tool for Spotting and Evading Troubles with Perfect Fluid Models

A review is given of various schemes for constructing models of rotating perfect fluid bodies in general relativity. Success in most of these endeavours is limited to either fluids of infinite extent or those matched to an asymptotically ill-behaved ambient vacuum domain or else, matched but infinitely thin bodies. There is an obvious need to find physical or mathematical guiding principles that confine this research so as to focus on the properties of the field established by these principles. The suggestion is to use the slow-rotation limit for singling out the viable classes of models. This is fostered by recent results of our group, which enable us (i) to find the possible Petrov types, (ii) to exclude certain existing analytic solutions (among these the Wahlquist metric) from the candidates for matching to an asymptotically well-behaved vacuum domain and (iii) to construct, in fact, global models of slowly rotating fluid bodies.