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The Ernst equation and the Riemann-Hilbert problem on hyperelliptic Riemann surfaces

✍ Scribed by C. Klein; O. Richter

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
405 KB
Volume
24
Category
Article
ISSN
0393-0440

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✦ Synopsis

We discuss a class of solutions to the Ernst equation (the stationary axisymmetric Einstein equations) obtained as solutions of a generalized scalar Riemann-Hilbert problem on a hyperelliptic Riemann surface. The singular structure of these solutions is studied for arbitrary genus of the Riemann surface. A subclass is given for which the Ernst potential is everywhere regular besides at a contour that can be identified with the surface of a body of revolution. It turns out that the recently discussed rigidly rotating dust disk belongs to this class.

πŸ“œ SIMILAR VOLUMES

A remark on the Riemann-Hilbert problem
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## Abstract This paper concerns the existence of nontrivial solutions of the Riemann‐Hilbert problem with a continuous coefficient whose values belong to two rays in the complex plane. Our results extend those recently obtained by E. Shargorodsky and J. F. Toland [6]. (Β© 2004 WILEY‐VCH Verlag GmbH

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This paper presents and studies Fredholm integral equations associated with the linear Riemann-Hilbert problems on multiply connected regions with smooth boundary curves. The kernel of these integral equations is the generalized Neumann kernel. The approach is similar to that for simply connected re