Lecture note 29/2006

Ernst Equation and Riemann Surfaces - Analytical and Numerical Methods

Christian Klein and Olaf Richter

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Submission date: 12. Jan. 2006
Pages: 259
published as:
Klein, Chr. and O.Richter (eds.): Ernst equation and Riemann surfaces : analytical and numerical methods
   Berlin [u.a.] : Springer, 2005. - X, 249 p.
   (Lecture notes in physics ; 685)
   ISBN 978-3-540-28589-2 - ISBN 3-540-28589-x       
Bibtex
MSC-Numbers: 83C15, 37K20
PACS-Numbers: 04.20.Jb
Download full preprint: PDF (7416 kB)

Abstract:
Exact solutions to Einstein's equations have been useful for the understanding of general relativity in many respects. They have led to physical concepts as black holes and event horizons and helped to visualize interesting features of the theory. In addition they have been used to test the quality of various approximation methods and numerical codes. The most powerful solution generation methods are due to the theory of Integrable Systems. In the case of axisymmetric stationary spacetimes the Einstein equations are equivalent to the completely integrable Ernst equation. In this volume these solutions to the Ernst equation are studied in detail and physical and mathematical aspects of this class are discussed both analytically and numerically.The original publication is available at Springer-Online: www.springeronline.com/3-540-28589-X.

03.07.2017, 01:40