Rotating fluid masses in general relativity. II

Abstract We describe some properties of a stationary, isolated, axially symmetric, rotating body of perfect fluid, according to general relativity. We first specialize to the case of constant specific entropy and constant angular velocity. The latter condition is equivalent to rigidity in the Born sense; both conditions are consequences of a simple variational principle. The hydrodynamic equations can then be integrated completely. Analogous first integrals are given also for the case of differential rotation. No use is made of the full field equations.