Christian Klein, Olaf Richter

Ernst Equation and Riemann Surfaces

Analytical and Numerical Methods

• Gebundenes Buch

Produktbeschreibung

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.

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Produktdetails

• Lecture Notes in Physics 685
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 11540953, 978-3-540-28589-2
• 2005
• Seitenzahl: 264
• Erscheinungstermin: 18. November 2005
• Englisch
• Abmessung: 241mm x 160mm x 19mm
• Gewicht: 520g
• ISBN-13: 9783540285892
• ISBN-10: 354028589X
• Artikelnr.: 15012530

Autorenporträt

Christian Klein, MPI für Mathematik in den Naturwissenschaften, Leipzig, Germany

Inhaltsangabe

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.

Rezensionen

From the reviews: "This book covers these areas - the reduction of the Einstein vacuum equations to the Ernst equation, the reinterpretation of the Ernst equation as an integrable system and the use of techniques of integrable systems ... . This book provides an excellent exposition of these ideas; as well as providing a sound introduction ... . This is an excellently written monograph with an encyclopedic list of references and it should be of interest to a wide range of people ... ." (Ian A. B. Strachan, Mathematical Reviews, Issue 2006 k) "What the present book describes are some of the heroic efforts that have been undertaken to construct physically significant spacetimes by solving the vacuum Ernst equation. ... It is the reviewer's opinion that the resulting book will be more useful as a resource for those who are already well versed in the subject of integrable systems ... ." (Frederick J Ernst, Classical and Quantum Gravity, Vol. 24, 2007)