Authors:
- Examines in detail the solutions to the Ernst equation associated to Riemann surfaces
- Physical and mathematical aspects of this class are discussed both analytically and numerically
- This is the only broad survey in this topic related to general relativity and solutions to Einstein equations of astrophysical relevance
- The text will be of interest to lecturers, researchers and graduate students
Part of the book series: Lecture Notes in Physics (LNP, volume 685)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
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)
Bibliographic Information
Book Title: Ernst Equation and Riemann Surfaces
Book Subtitle: Analytical and Numerical Methods
Authors: Christian Klein
Series Title: Lecture Notes in Physics
DOI: https://doi.org/10.1007/11540953
Publisher: Springer Berlin, Heidelberg
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2005
Hardcover ISBN: 978-3-540-28589-2Published: 18 November 2005
Softcover ISBN: 978-3-642-06677-1Published: 22 October 2010
eBook ISBN: 978-3-540-31513-1Published: 26 November 2005
Series ISSN: 0075-8450
Series E-ISSN: 1616-6361
Edition Number: 1
Number of Pages: X, 249
Topics: Mathematical Methods in Physics, Classical and Quantum Gravitation, Relativity Theory, Differential Geometry