Ernst Equation and Riemann Surfaces
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 the solutions to the Ernst equation associated to Riemann surfaces are studied in detail and physical and mathematical aspects of this class are discussed both analytically and numerically.
Examines in detail the solutions to the Ernst equation associated to Riemann surfacesPhysical and mathematical aspects of this class are discussed both analytically and numericallyThis is the only broad survey in this topic related to general relativity and solutions to Einstein equations of astrophysical relevanceThe text will be of interest to lecturers, researchers and graduate students