Contents

pp v-xii

The scope of this text

pp xiii-xiv

Preface to the second edition

pp xv-xvii

Acknowledgments

pp xviii-xviii

1 - How the theory of relativity came into being (a brief historical sketch)

pp 1-6

Part I - Elements of differential geometry

pp 7-8

2 - A short sketch of 2-dimensional differential geometry

pp 9-11

3 - Tensors, tensor densities

pp 12-23

4 - Covariant derivatives

pp 24-30

5 - Parallel transport and geodesic lines

pp 31-33

6 - The curvature of a manifold; at manifolds

pp 34-44

7 - Riemannian geometry

pp 45-68

8 - Symmetries of Riemann spaces, invariance of tensors

pp 69-88

9 - Methods to calculate the curvature quickly: differential forms and algebraic computer programs

pp 89-93

10 - The spatially homogeneous Bianchi-type spacetimes

pp 94-107

11 - * The Petrov classication by the spinor method

pp 108-120

Part II - The theory of gravitation

pp 121-122

12 - The Einstein equations and the sources of a gravitational field

pp 123-155

13 - The Maxwell and Einstein–Maxwell equations and the Kaluza–Klein theory

pp 156-161

14 - Spherically symmetric gravitational fields of isolated objects

pp 162-210

15 - Relativistic hydrodynamics and thermodynamics

pp 211-222

16 - Relativistic cosmology I: general geometry

pp 223-254

17 - Relativistic cosmology II: the Robertson–Walker geometry

pp 255-288

18 - Relativistic cosmology III: the LemaÎtre–Tolman geometry

pp 289-365

19 - Relativistic cosmology IV: simple generalisations of L–T and related geometries

pp 366-390

20 - Relativistic cosmology V: the Szekeres geometries

pp 391-441

21 - The Kerr metric

pp 442-498

22 - Relativity enters technology: the Global Positioning System

pp 499-510

23 - Subjects omitted from this book

pp 511-513