On a Class of Physically Realistic Solutions to the Ernst Equation

Within a class of algebro-geometric solutions to the Ernst equation we identify a physically interesting subclass: The solutions are regular except at a closed surface, asymptotically flat, and equatorially symmetric. This suggests that they could describe the exterior of an isolated body, for instance, a relativistic star or a galaxy. Within this class, one has the freedom to specify a real function and a set of complex parameters that can possibly be used to solve certain boundary value problems for the Ernst equation such as the rigidly rotating dust disk. The solutions can have ergoregions, a Minkowskian limit, and an ultrarelativistic limit where the metric approaches the extreme Kerr solution.