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.

On the black hole limit of rotating discs and rings

“…See[17] for a discussion of the extension of the Kerr uniqueness proof to the case with a degenerate horizon 2. Throughout the paper we use units in which the speed of light as well as Newton's gravitational constant are equal to 1.…”