Stationary stars are axisymmetric

The final state of thermonuclear evolution of a star may consist of either a black hole or an ''ordinary'' star such as a white dwarf or neutron star. For the case of black holes, a great deal is known about the structure of this final stationary state; in particular, Hawking has shown that stationary black holes are axisymmetric. An extension of this result is presented which includes the ''ordinary'' final state of stars. It is shown that a stationary star, consisting of a viscous heat-conducting general-relativistic fluid, must be axisymmetric. For this proof, the star is assumed to be embedded in an asymptotically Minkowskian spacetime manifold. The functions which describe the geometry and the fluid of the star are assumed to satisfy certain smoothness conditions