Ernst equation and Riemann surfaces : analytical and numerical methods /
Klein, Christian.
Ernst equation and Riemann surfaces : analytical and numerical methods / Christian Klein, Olaf Richter. - Berlin ; New York : Springer, ©2005. - 1 online resource (x, 249 pages) : illustrations - Lecture notes in physics, 685 0075-8450 ; . - Lecture notes in physics ; 685. .
Includes bibliographical references (pages 237-245) and index.
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."--Jacket
9783540315131 3540315136
10.1007/11540953 doi
978-3-540-28589-2 Springer http://www.springerlink.com
Riemann surfaces.
Einstein field equations.
Differential equations, Partial.
Surfaces de Riemann.
Équations aux dérivées partielles.
Équations du champ d'Einstein.
Physique.
Differential equations, Partial
Einstein field equations
Riemann surfaces
QA333 / .K54 2005eb
515.353
Ernst equation and Riemann surfaces : analytical and numerical methods / Christian Klein, Olaf Richter. - Berlin ; New York : Springer, ©2005. - 1 online resource (x, 249 pages) : illustrations - Lecture notes in physics, 685 0075-8450 ; . - Lecture notes in physics ; 685. .
Includes bibliographical references (pages 237-245) and index.
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."--Jacket
9783540315131 3540315136
10.1007/11540953 doi
978-3-540-28589-2 Springer http://www.springerlink.com
Riemann surfaces.
Einstein field equations.
Differential equations, Partial.
Surfaces de Riemann.
Équations aux dérivées partielles.
Équations du champ d'Einstein.
Physique.
Differential equations, Partial
Einstein field equations
Riemann surfaces
QA333 / .K54 2005eb
515.353