Rotating equilibrium configurations in Einstein's theory of gravitation

The theory of figures of equilibrium of rotating fluids arose from geophysical and astrophysical considerations. Within Newton's theory of gravitation, Maclaurin (1742) found the axially symmetric and stationary solution to the problem in the case of constant mass-density: a sequence of oblate spheroids. In the limit of maximum ellipticity a rotating disk is obtained. By applying analytical solution techniques from soliton theory this Maclaurin disk has been "continued" to Einstein's theory of gravitation [1, 2, 3]. After an introduction into these developments, the parametric collapse to a rotating black hole and possible generalizations axe discussed.