Book contents
- Frontmatter
- Contents
- Preface
- Notation
- 1 Rotating fluid bodies in equilibrium: fundamental notions and equations
- 2 Analytical treatment of limiting cases
- 3 Numerical treatment of the general case
- 4 Remarks on stability and astrophysical relevance
- Appendix 1 A detailed look at the mass-shedding limit
- Appendix 2 Theta functions: definitions and relations
- Appendix 3 Multipole moments of the rotating disc of dust
- Appendix 4 The disc solution as a Bäcklund limit
- References
- Index
Preface
Published online by Cambridge University Press: 22 October 2009
- Frontmatter
- Contents
- Preface
- Notation
- 1 Rotating fluid bodies in equilibrium: fundamental notions and equations
- 2 Analytical treatment of limiting cases
- 3 Numerical treatment of the general case
- 4 Remarks on stability and astrophysical relevance
- Appendix 1 A detailed look at the mass-shedding limit
- Appendix 2 Theta functions: definitions and relations
- Appendix 3 Multipole moments of the rotating disc of dust
- Appendix 4 The disc solution as a Bäcklund limit
- References
- Index
Summary
The theory of figures of equilibrium of rotating, self-gravitating fluids was developed in the context of questions concerning the shape of the Earth and celestial bodies. Many famous physicists and mathematicians such as Newton, Maclaurin, Jacobi, Liouville, Dirichlet, Dedekind, Riemann, Roche, Poincaré, H. Cartan, Lichtenstein and Chandrasekhar made important contributions. Within Newton's theory of gravitation, the shape of the body can be inferred from the requirement that the force arising from pressure, the gravitational force and the centrifugal force (in the corotating frame) be in equilibrium. Basic references are the books by Lichtenstein (1933) and Chandrasekhar (1969).
Our intention with the present book is to treat the general relativistic theory of equilibrium configurations of rotating fluids. This field of research is also motivated by astrophysics: neutron stars are so compact that Einstein's theory of gravitation must be used for calculating the shapes and other physical properties of these objects. However, as in the books mentioned above, which inspired this book to a large extent, we want to present the basic theoretical framework and will not go into astrophysical detail. We place emphasis on the rigorous treatment of simple models instead of trying to describe real objects with their many complex facets, which by necessity would lead to ephemeral and inaccurate models.
The basic equations and properties of equilibrium configurations of rotating fluids within general relativity are described in Chapter 1.
- Type
- Chapter
- Information
- Relativistic Figures of Equilibrium , pp. vii - viiiPublisher: Cambridge University PressPrint publication year: 2008