Relativistic Figures of Equilibrium

Relativistic Figures of Equilibrium

by Reinhard Meinel, Marcus Ansorg, Andreas Kleinwachter, Gernot Neugebauer
     
 

ISBN-10: 052186383X

ISBN-13: 9780521863834

Pub. Date: 06/26/2008

Publisher: Cambridge University Press

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…  See more details below

Overview

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.

Product Details

ISBN-13:
9780521863834
Publisher:
Cambridge University Press
Publication date:
06/26/2008
Pages:
228
Product dimensions:
6.85(w) x 9.72(h) x 0.59(d)

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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