TY  - BOOK
AU  - Klein,Christian
AU  - Richter,Olaf
TI  - Ernst equation and Riemann surfaces: analytical and numerical methods 
T2  - Lecture notes in physics,
SN  - 9783540315131
AV  - QA333 .K54 2005eb
U1  - 515.353 22
PY  - 2005///
CY  - Berlin, New York
PB  - Springer
KW  - Riemann surfaces
KW  - Einstein field equations
KW  - Differential equations, Partial
KW  - Surfaces de Riemann
KW  - Équations aux dérivées partielles
KW  - Équations du champ d'Einstein
KW  - Physique
KW  - eclas
KW  - fast
N1  - 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
N2  - "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
UR  - https://link-springer-com.libraryproxy.ist.ac.at/10.1007/11540953
ER  -