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Lecture Notes in Physics

Ernst Equation and Riemann Surfaces

Analytical and Numerical Methods

Authors: Klein, Christian, Richter, Olaf

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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)


Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $74.99
price for USA in USD (gross)
  • The eBook version of this title will be available soon
  • ISBN 978-3-540-31513-1
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA in USD
  • ISBN 978-3-540-28589-2
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $84.99
price for USA in USD
  • ISBN 978-3-642-06677-1
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Ernst Equation and Riemann Surfaces
Book Subtitle
Analytical and Numerical Methods
Authors
Series Title
Lecture Notes in Physics
Series Volume
685
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-31513-1
DOI
10.1007/11540953
Hardcover ISBN
978-3-540-28589-2
Softcover ISBN
978-3-642-06677-1
Series ISSN
0075-8450
Edition Number
1
Number of Pages
X, 249
Topics

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