Ernst Equation and Riemann Surfaces: Analytical and Numerical Methods / Edition 1

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Overview

Exact solutions to Einstein’s equations have been useful for the understanding of general relativity in many respects. They have led to such physical concepts as black holes and event horizons, and helped to visualize interesting features of the theory. This volume studies the solutions to the Ernst equation associated to Riemann surfaces in detail. In addition, the book discusses the physical and mathematical aspects of this class analytically as well as numerically.

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Editorial Reviews

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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)

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Product Details

  • ISBN-13: 9783642066771
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 12/15/2010
  • Series: Lecture Notes in Physics Series , #685
  • Edition description: Softcover reprint of hardcover 1st ed. 2005
  • Edition number: 1
  • Pages: 251
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.55 (d)

Table of Contents

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.

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