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Lecture Note
29/2006
Ernst Equation and Riemann Surfaces - Analytical and Numerical Methods
Christian Klein and Olaf Richter
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.
