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Exact solutions to Einstein's equations have been useful for the understanding of general relativity in many respects. They have led to such physical concepts as black holes and event horizons, and helped to visualize interesting features of the theory. This volume studies the solutions to the Ernst equation associated to Riemann surfaces in detail. In addition, the book discusses the physical and mathematical aspects of this class analytically as well as numerically.

Ernst Equation and Riemann Surfaces: Analytical and Numerical Methods

Introduction.- The Ernst Equation.- Riemann-Hilbert Problem and Fay's Identity.- Analyticity Properties and Limiting Cases.- Boundary Value Problems and Solutions.- Hyperelliptic Theta Functions and Spectral Methods.- Physical Properties.- Open Problems.- Riemann Surfaces and Theta Functions.- Ernst Equation and Twister Theory.- Index.