Ernst Equation and Riemann Surfaces

Analytical and Numerical Methods

  • Authors
  • Christian Klein

Part of the Lecture Notes in Physics book series (LNP, volume 685)

Table of contents

  1. Front Matter
  2. Christian Klein
    Pages 1-15
  3. Christian Klein
    Pages 17-42
  4. Christian Klein
    Pages 79-96
  5. Christian Klein
    Pages 97-121
  6. Christian Klein
    Pages 147-171
  7. Christian Klein
    Pages 173-189
  8. Christian Klein
    Pages 237-245
  9. 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.


Einstein equations Ernst equation Kerr metric Relativity ayxisymmetric general relativity

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