文档介绍：The large scale
structure
ofspace-time
& G. . ELLIS
CAMBRIDGE MONOGRAPHS ON
MATHEMATICAL PHYSICS
THE LARGE SCALE STRUCTURE
OF SPACE-TIME
S. W. HAWKING, .
Lucasian Professor of Mathematics in the University ofCambridge and
Fellow ofConville and Caius College
AND
G. F. R. ELLIS
Professor of Mathematics, University ofCape Town
,"':i.. CAMBRIDGE
::: UNIVERSITY PRESS
Published by the Press Syndicate ofthe University ofCambridge
The Pitt Building, Trumpington Street, Cambridge CB2 IRP
40 West 20th Street, New York, NY 10011-4211, USA
10 Stamford Road. Oakleigh. Melbourne 3166. Australia
C Cambridge University Press 1973
F~tpublishedl973
First paperback edition 1974
Reprinted 1976. . . 1986.
1987. 1989. 1991. 1993 (twice). 1994,
Printed in the United States of America
Library of Congress Catalogue card number: 72-93671
ISBN 0-521-09906-4 paperback
To
Contents
Preface page xi
1 The role of gravity 1
2 Differential geometry 10
Manifolds 11
Vectors and tensors 15
Maps of manifolds 22
Exterior differentiation and the Lie derivative 24
Covariant differentiation and the curvature tensor 30
The metric 36
Hypersurfaces 44
The -volume element and Gauss' theorem 47
Fibre bundles 50
3 General Relativity 56
The space-time manifold 56
The matter fields 59
Lagrangian formulation 64
The field equations 71
4 The physical significance of curvature 78
Timelike curves 78
Null curves 86
Energy conditions - 88
Conjugate points 96
Variation of arc-length 102
5 Exact solutions 117
Minkowski space-time 118
De Sitter and anti-de Sitter space-times 124
Robertson-Walker spaces 134
Spatially homogeneous cosmological models 142
[ vii]
CONTENTS
The Schwarzschild and Reissner-Nordstrom
solutions page 149
The Kerr solution 161
Godel's uni