Quasistationary collapse to the extreme Kerr black hole

It is shown that the extreme Kerr black hole is the only candidate for a black hole limit of rotating fluid bodies in equilibrium.Comment: 6 pages, submitted to Annalen der Physik (Leipzig

Relativistic figures of equilibrium: from Maclaurin spheroids to Kerr black holes

Analytical and numerical results on equilibrium configurations of rotating fluid bodies within Einstein's theory of gravitation are reviewed. Particular emphasis is placed on continuous parametric transitions to black holes. In this connection the uniqueness of extremal Kerr black holes is discussed.Comment: 3 pages, talk given at the Twelfth Marcel Grossmann Meeting (Paris, July 12 - 18, 2009), submitted to the Conference Proceedings, v3: references update

Uniformly rotating axisymmetric fluid configurations bifurcating from highly flattened Maclaurin spheroids

We give a thorough investigation of sequences of uniformly rotating, homogeneous axisymmetric Newtonian equilibrium configurations that bifurcate from highly flattened Maclaurin spheroids. Each one of these sequences possesses a mass-shedding limit. Starting at this point, the sequences proceed towards the Maclaurin sequence and beyond. The first sequence leads to the well known Dyson rings, whereas the end points of the higher sequences are characterized by the formation of a two-body system, either a core-ring system (for the second, the fourth etc. sequence) or a two-ring system (for the third, the fifth etc. sequence). Although the general qualitative picture drawn by Eriguchi and Hachisu in the eighties has been confirmed, slight differences turned out in the interpretation of the origin of the first two-ring sequence and in the general appearance of fluid bodies belonging to higher sequences.Comment: 10 pages, 11 figures, 5 tables, submitted to MNRA