Einstein's Space-Time: An Introduction to Special and General Relativity

Cover......Page 1
Einstein’s Space-Time An Introduction to Special and General Relativity......Page 3
Preface......Page 5
Preface to the English Edition......Page 8
Contents......Page 9
List of Complements......Page 13
List of Biographies......Page 14
front-matter.pdf......Page 2
Absolute Space and Time......Page 15
Geometric Properties of the Space......Page 16
Galileo and the Laws of Motion......Page 18
Change of Coordinates Between Frames in Relative Motion......Page 20
Principle of Inertia......Page 22
Principle of Relativity......Page 23
Physical Phenomena Having a Privileged Reference System......Page 25
Maxwell\'s Electromagnetism......Page 27
Two Models for the Light......Page 31
First Determination of the Speed of Light......Page 35
The Aberration of Light......Page 36
First Terrestrial Method to Measure c......Page 40
The Luminiferous Ether......Page 41
Searching for the Absolute Terrestrial Motion: Dragging of Ether......Page 42
Fizeau\'s Experiment......Page 46
Hoek\'s Experiment......Page 47
Airy\'s Experiment......Page 49
Michelson--Morley Experiment......Page 50
FitzGerald--Lorentz Length Contraction......Page 56
The Twilight of the Ether......Page 58
Postulates of Special Relativity......Page 61
Length Contractions and Time Dilatations......Page 63
The Muon Journey......Page 66
Lengths Transversal to Motion......Page 67
Composition of Motions......Page 68
Interpretation of Fizeau\'s Experiment......Page 71
The Notion of Simultaneity......Page 72
Events and World Lines......Page 76
Coordinate Lines of S in the Space-Time Diagram of S......Page 79
Lorentz Transformations......Page 83
Comparing Clocks in Different Frames......Page 88
Velocity and Acceleration Transformations......Page 92
``Paradoxes\'\': Remnants of Classical Thought......Page 95
Doppler Effect......Page 100
Transformation of Light Rays......Page 104
Transformation of a Plane Wave......Page 106
Propagation of Light in Material Media......Page 109
Interval......Page 111
Calibration Hyperbola......Page 112
Light Cone......Page 114
Timelike-Separated Events......Page 115
Twin Paradox......Page 117
Spacelike-Separated Events......Page 121
Velocity Parameter: Rapidity......Page 123
Wigner Rotation......Page 125
The Electromagnetic Plane Wave......Page 131
Transformation of E and B......Page 133
Charge and Current Transformations......Page 136
Field of a Uniformly Moving Charge......Page 140
Transformation of Potentials......Page 141
Fields in Material Media......Page 142
Moving Dipoles Fields......Page 144
Lorentz Force Transformation......Page 146
Electromagnetic Field Invariants......Page 147
Conservation Laws......Page 149
Energy and Momentum of a Particle......Page 151
Energy--Momentum Invariant. Force......Page 155
Charge Movement in Uniform Fields......Page 157
Center-of-Momentum Frame......Page 160
Phenomena Derived from Mass--Energy equivalence......Page 162
Center of Inertia......Page 167
Elastic Collisions......Page 169
Interaction Between Electromagnetic Radiation and Matter......Page 177
Four-Tensors......Page 185
Metric......Page 190
Four-vector ``norm\'\' and Argument......Page 194
Angular Momentum......Page 195
Volume and hypersurfaces......Page 198
Energy--Momentum Tensor of Continuous Media......Page 202
Electromagnetism......Page 211
Fermi--Walker Transport......Page 216
The Criticism of Absolute Motion......Page 221
The Principle of Equivalence......Page 224
The Inertial--Gravitational Field......Page 229
Riemannian Geometry......Page 234
Motion of a Freely Gravitating Particle......Page 237
Covariant Derivative. Minimal coupling......Page 241
Riemann Tensor. Einstein Equations......Page 248
Schwarzschild solution. Black hole......Page 256
Inertial Movement in Schwarzschild Geometry......Page 260
Light Deflection in Schwarzschild Geometry......Page 264
Kruskal-Szekeres Coordinates......Page 266
Cosmological Models......Page 269
Evolution of the Universe......Page 277
Non-Machian Solutions. Cosmological Constant......Page 285
Problems of the Standard Big-Bang Model......Page 291
Experimental Tests......Page 295
Euler--Lagrange Equation......Page 300
The Action Functional......Page 301
Metric Energy--Momentum Tensor......Page 304
Gauge Transformations and Source Conservation......Page 305
Killing Vectors and Energy--Momentum Conservation......Page 307
Bibliography......Page 309
Cited Papers......Page 311
Index......Page 315