Relativistic Figures of Equilibrium: Mathematical Models of Rotating Fluid Bodies in Gravitational Theory

This article is concerned with models of rotating bodies which are composed of fluid matter and whose internal structure is determined to a great extent by its own gravitational field. In particular, these models exhibit an equilibrium between attracting gravitational forces, repelling pressure and centrifugal forces. By virtue of this balance of forces the body takes on a typical shape: a figure of equilibrium. In the following it is described which principle physical and mathematical aspects arise and, moreover, the complexity of this field is demonstrated by means of a number of examples.