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 Bäcklund 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 Bäcklund-type solutions. As a further result, we find that, in contrast with the Laplace equation, arbitrary boundary values may not be prescribed.
- Received 28 September 2001
DOI:https://doi.org/10.1103/PhysRevD.65.044006
©2002 American Physical Society