Ernst Equation and Riemann Surfaces

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The book delves into the significance of exact solutions to Einstein's equations in understanding general relativity, exploring concepts like black holes and event horizons. It emphasizes the role of Integrable Systems theory in generating solutions, particularly focusing on the Ernst equation for axisymmetric stationary spacetimes. Detailed analyses of solutions related to Riemann surfaces are presented, covering both physical and mathematical aspects through analytical and numerical methods, providing insights into the complexities of spacetime.