Relativistic Figures of Equilibrium

by Reinhard Meinel , Marcus Ansorg , Andreas Kleinwächter , Gernot Neugebauer , David Petroff

• ISBN13: 9780521863834
• ISBN10: 052186383X
• Format: Hardcover
• Copyright: 2008-07-14
• Publisher: Cambridge University Press

Summary

In recent years, the study of neutron stars and black holes has become increasingly important, and rigorous mathematical analysis needs to be applied in order to understand their basic physics. This book treats the classical problem of gravitational physics within Einstein's theory of general relativity. It presents basic principles and equations needed to describe rotating fluid bodies, as well as black holes in equilibrium. It then goes on to deal with a number of analytically tractable limiting cases, placing particular emphasis on the rigidly rotating disc of dust. The book concludes by considering the general case using powerful numerical methods that are applied to various models, including the classical example of equilibrium figures of constant density. Researchers in general relativity, mathematical physics, and astrophysics will find this a valuable reference book on the topic. A related website containing codes for calculating various figures of equilibrium is available at www.cambridge.org/9780521863834.

Author Biography

Gernot Neugebauer is a Professor Emeritus at the Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitat.

Table of Contents

Preface	p. vii
Notation	p. ix
Rotating fluid bodies in equilibrium: fundamental notions and equations	p. 1
The concept of an isolated body	p. 1
Fluid bodies in equilibrium	p. 3
The metric of an axisymmetric perfect fluid body in stationary rotation	p. 3
Einstein's field equations inside and outside the body	p. 5
Equations of state	p. 10
Physical properties	p. 13
Limiting cases	p. 16
Transition to black holes	p. 26
Analytical treatment of limiting cases	p. 34
Maclaurin spheroids	p. 34
Schwarzschild spheres	p. 38
The rigidly rotating disc of dust	p. 40
The Kerr metric as the solution to a boundary value problem	p. 108
Numerical treatment of the general case	p. 114
A multi-domain spectral method	p. 115
Coordinate mappings	p. 128
Equilibrium configurations of homogeneous fluids	p. 137
Configurations with other equations of state	p. 153
Fluid rings with a central black hole	p. 166
Remarks on stability and astrophysical relevance	p. 177
A detailed look at the mass-shedding limit	p. 181
Theta functions: definitions and relations	p. 187
Multipole moments of the rotating disc of dust	p. 193
The disc solution as a Backlund limit	p. 203
References	p. 208
Index	p. 216
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