Relativistic Figures of Equilibrium

Reinhard Meinel; Marcus Ansorg; Andreas Kleinwächter; Gernot Neugebauer; David Petroff

doi:10.1017/CBO9780511535154

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/9781107407350.

Review of the hardback:'… this book is a very valuable tool for anybody wishing to learn more about relativistic rotating bodies in equilibrium. … overall it is an excellent reference on this topic.'

Source: Classical and Quantum Gravity

Review of the hardback:'This is an advanced and specialised book, presenting the state of the art in this field, with emphasis on the authors' own expertise and approaches. It contains an extensive discussion of the analytical handling of limiting cases on the one hand and the numerical treatment of the general case on the other, thus providing a complete picture of the subject. … pleasant to read …This book is a standard reference for this subject every researcher in relativity theory should know.'

Source: General Relativity and Gravitation

Review of the hardback:'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.'

Source: Mathematical Reviews

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Relativistic Figures of Equilibrium

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Notation
pp ix-x

1 - Rotating fluid bodies in equilibrium: fundamental notions and equations
pp 1-33

2 - Analytical treatment of limiting cases
pp 34-113

3 - Numerical treatment of the general case
pp 114-176

4 - Remarks on stability and astrophysical relevance
pp 177-180

Appendix 1 - A detailed look at the mass-shedding limit
pp 181-186

Appendix 2 - Theta functions: definitions and relations
pp 187-192

Appendix 3 - Multipole moments of the rotating disc of dust
pp 193-202

Appendix 4 - The disc solution as a Bäcklund limit
pp 203-207

References
pp 208-215

Index
pp 216-218

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Relativistic Figures of Equilibrium

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