Ernst Equation and Riemann Surfaces

Analytical and Numerical Methods
Softcover version of original hardcover Auflage 2005
ISBN: 978-3-642-06677-1
Verlag: Springer

Buch, Englisch, 249 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 406 g

Reihe: Lecture Notes in Physics

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.

Zielgruppe

Research

Autoren/Hrsg.

Richter, Olaf

Klein, Christian

Fachgebiete

• Naturwissenschaften Physik Quantenphysik Relativität, Gravitation
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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.