Relativistic figures of equilibrium / Reinhard Meinel ... [and others].

Format:

Book

Contributor:

Meinel, Reinhard.

Language:

English

Subjects (All):

Rotating masses of fluid.

Equilibrium.

Relativity (Physics).

Astrophysics.

Physical Description:

ix, 218 pages : illustrations ; 26 cm

Place of Publication:

Cambridge, UK ; New York : Cambridge University Press, 2008.

Summary:

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.

This book treats the classical problem of gravitational physics within Einstein's theory of general relativity. It begins by presenting 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.

Contents:

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.

Notes:

Includes bibliographical references (pages 208-215) and index.

ISBN:

9780521863834

052186383X

OCLC:

213400615

Online:

Contributor biographical information

Publisher description