Dirichlet Boundary Value Problems of the Ernst Equation
Marcus Ansorg, Andreas Kleinwächter, Reinhard Meinel, Gernot Neugebauer
Abstract
We demonstrate how the solution to an exterior Dirichlet boundary value problem of the axisymmetric, stationary Einstein equations can be found in terms of generalized solutions of the Backlund type. The proof that this generalization procedure is valid is given, which also proves conjectures about earlier representations of the gravitational field corresponding to rotating disks of dust in terms of Backlund type solutions.