In a recent paper we presented analytic expressions for the axis potential, the disk metric, and the surface mass density of the global solution to Einstein's field equations describing a rigidly rotating disk of dust. Here we add the complete solution in terms of ultraelliptic functions and quadratures. 04.20.Jb, 95.30.Sf Typeset using REVT E X 1

Ever since Newton introduced his theory of gravity, many famous physicists and mathematicians have worked on the problem of determining the properties of rotating bodies in equilibrium, such as planets and stars. In recent years, neutron stars and black holes have become increasingly important, and observations by astronomers and modelling by astrophysicists have reached the stage where rigorous mathematical analysis needs to be applied in order to understand their basic physics. This book treats the classical problem of gravitational physics within Einstein's theory of general relativity. It begins by presenting basic principles and equations needed to describe rotating fluid bodies, as well as black holes in equilibrium. It then goes on to deal with a number of analytically tractable limiting cases, placing particular emphasis on the rigidly rotating disc of dust. The book concludes by considering the general case, using powerful numerical methods that are applied to various models, including the classical example of equilibrium figures of constant density. Researchers in general relativity, mathematical physics and astrophysics will find this a valuable reference book on the topic. A related website containing codes for calculating various figures of equilibrium is available at www.cambridge. org/9780521863834.

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Abstract. We give a detailed description of the recently developed multi-domain spectral method for constructing highly accurate general-relativistic models of rapidly rotating stars. For both "ordinary" and "critical" configurations, we show using representative examples, how the accuracy improves as the order of the approximation increases. As well as homogeneous fluid bodies, we also discuss models of polytropic and strange stars.