Relativistic Figures of Equilibrium

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Ever since Newton introduced his theory of gravity, many famous physicists and mathematicians have worked on the problem of determining the properties of rotating bodies in equilibrium, such as planets and stars. In recent years, neutron stars and black holes have become increasingly important, and observations by astronomers and modelling by astrophysicists have reached the stage where rigorous mathematical analysis needs to be applied in order to understand their basic physics.
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Editorial Reviews

From the Publisher
"... A rigorous treatment of the simple models using both analytical and numerical methods."
Book News

"Nicely produced by Cambridge University Press, this rather specialized book rich in analytical and numerical methods is of value to students and professional researchers in general relativity, mathematical physics and astrophysics."
Gerard A. Maugin, Mathematical Reviews

"The results of this book are of importance for a better understanding of the state of the dynamics of astrophysical objects, which will influence, among others, future high precision observations and the calculation of gravitational wave templates."
General Relativity and Gravitation

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Product Details

  • ISBN-13: 9780521863834
  • Publisher: Cambridge University Press
  • Publication date: 6/26/2008
  • Pages: 228
  • Product dimensions: 6.85 (w) x 9.72 (h) x 0.59 (d)

Meet the Author

Reinhard Meinel is a Professor of Theoretical Physics at the Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität, Jena, Germany. His research is in the field of gravitational theory, focusing on astrophysical applications.

Marcus Ansorg is a Researcher at the Max-Planck-Institut für Gravitationsphysik, Potsdam, Germany, where his research focuses on the application of spectral methods for producing highly accurate solutions to Einstein's field equations.

Andreas Kleinwächter is a Researcher at the Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität. His current research is on analytical and numerical methods for solving the axisymmetric and stationary equations of general relativity.

Gernot Neugebauer is a Professor Emeritus at the Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität. His research deals with Einstein's theory of gravitation, soliton theory, and thermodynamics.

David Petroff is a Researcher at the Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität. His research is on stationary black holes and neutron stars, making use of analytical approximations and numerical methods.

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Table of Contents

Preface vii

Notation ix

1 Rotating fluid bodies in equilibrium: fundamental notions and equations 1

1.1 The concept of an isolated body 1

1.2 Fluid bodies in equilibrium 3

1.3 The metric of an axisymmetric perfect fluid body in stationary rotation 3

1.4 Einstein's field equations inside and outside the body 5

1.5 Equations of state 10

1.6 Physical properties 13

1.7 Limiting cases 16

1.8 Transition to black holes 26

2 Analytical treatment of limiting cases 34

2.1 Maclaurin spheroids 34

2.2 Schwarzschild spheres 38

2.3 The rigidly rotating disc of dust 40

2.4 The Kerr metric as the solution to a boundary value problem 108

3 Numerical treatment of the general case 114

3.1 A multi-domain spectral method 115

3.2 Coordinate mappings 128

3.3 Equilibrium configurations of homogeneous fluids 137

3.4 Configurations with other equations of state 153

3.5 Fluid rings with a central black hole 166

4 Remarks on stability and astrophysical relevance 177

Appendix 1 A detailed look at the mass-shedding limit 181

Appendix 2 Theta functions: definitions and relations 187

Appendix 3 Multipole moments of the rotating disc of dust 193

Appendix 4 The disc solution as a Backlund limit 203

References 208

Index 216

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