A student's guide to general relativity

Contents......Page 7
Preface......Page 8
Acknowledgements......Page 12
 1.1 Three Principles......Page 13
 1.2 Some Thought Experiments on Gravitation......Page 18
 1.3 Covariant Differentiation......Page 23
 1.4 A Few Further Remarks......Page 24
 Exercises......Page 28
 2.1 Linear Algebra......Page 30
 2.2 Tensors, Vectors, and One-Forms......Page 32
 2.3 Examples of Bases and Transformations......Page 48
 2.4 Coordinates and Spaces......Page 53
 Exercises......Page 54
 3.1 The Tangent Vector......Page 57
 3.2 Covariant Differentiation in Flat Spaces......Page 64
 3.3 Covariant Differentiation in Curved Spaces......Page 71
 3.4 Geodesics......Page 76
 3.5 Curvature......Page 79
 Exercises......Page 87
4 Energy, Momentum, and Einstein’s Equations......Page 96
 4.1 The Energy-Momentum Tensor......Page 97
 4.2 The Laws of Physics in Curved Space-time......Page 105
 4.3 The Newtonian Limit......Page 114
 Exercises......Page 120
 A.1 The Basic Ideas......Page 122
 A.2 The Postulates......Page 125
 A.3 Spacetime and the Lorentz Transformation......Page 127
 A.4 Vectors, Kinematics, and Dynamics......Page 133
 Exercises......Page 139
 B.1 The Schwarzschild Solution......Page 141
 B.2 The Perihelion of Mercury......Page 145
 B.3 Gravitational Waves......Page 148
 Exercises......Page 154
 C.2 Coordinates and Components......Page 156
 C.4 Differentiation......Page 157
 C.6 Einstein’s Summation Convention......Page 158
 C.7 Miscellaneous......Page 159
References......Page 160
Index......Page 162