Ernst Equation and Riemann Surfaces
Klein, Christian.
Ernst Equation and Riemann Surfaces Analytical and Numerical Methods / [electronic resource] : by Christian Klein. - X, 249 p. online resource. - Lecture Notes in Physics, 685 0075-8450 ; . - Lecture Notes in Physics, 685 .
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.
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.
9783540315131
10.1007/11540953 doi
Mathematical physics.
Global differential geometry.
Mathematical Methods in Physics.
Classical and Quantum Gravitation, Relativity Theory.
Differential Geometry.
QC5.53
530.15
Ernst Equation and Riemann Surfaces Analytical and Numerical Methods / [electronic resource] : by Christian Klein. - X, 249 p. online resource. - Lecture Notes in Physics, 685 0075-8450 ; . - Lecture Notes in Physics, 685 .
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.
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.
9783540315131
10.1007/11540953 doi
Mathematical physics.
Global differential geometry.
Mathematical Methods in Physics.
Classical and Quantum Gravitation, Relativity Theory.
Differential Geometry.
QC5.53
530.15