Dirichlet Boundary Value Problems of the Ernst Equation

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.

22 pages, to appear in Phys. Rev. D, Correction of a misprint in equation (4)

References in corpus (3)

• General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions
• Asymptotically flat solutions to the Ernst equation with reflection symmetry
• Solutions of Einstein's field equations related to Jacobi's inversion problem

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