Phys. Rev. D 65, 044006 (2002) [10 pages]Dirichlet boundary value problems of the Ernst equationReceived 28 September 2001; published 11 January 2002 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. © 2002 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.65.044006
DOI:
10.1103/PhysRevD.65.044006
PACS:
04.20.Jb, 04.25.Dm
|
|
About | Terms and Conditions | Subscriptions | Search | Help
Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement. Physical Review®, Physical Review Letters®, Reviews of Modern Physics®, and Physical Review Special Topics® are trademarks of the American Physical Society.