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

Abstract

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