Relativity : special, general, and cosmological / Wolfgang Rindler.

Format:

Book

Author/Creator:

Rindler, Wolfgang, 1924-2019.

Language:

English

Subjects (All):

Relativity (Physics).

Cosmology.

Physical Description:

xiii, 428 pages : illustrations ; 24 cm

Place of Publication:

Oxford ; New York : Oxford University Press, 2001.

Summary:

This text is a considerable amplification and modernization of the authors' earlier Essential Relativity. It brings relativity alive conceptually and emphasizes the foundations and the logical subtleties rather than the mathematics or the detailed experiments. It includes 300 exercises and promotes a visceral understanding and the confidence to tackle any fundamental relativistic problem. Following a critical overview of the whole field, special-relativistic kinematics is presented three dimensionally before the mathematical level gradually rises. Four vectors preceded mechanics, four tensors precede Maxwell theory, and three chapters on cosmology end the text. This book brings the challenge and excitement of modern relativity and cosmology at a rigorous mathematical level within the reach of advanced undergraduates, while containing enough new material to interest lecturers and researchers.

Contents:

1 From absolute space and time to influenceable spacetime: an overview 3

1.1 Definition of relativity 3

1.2 Newton's laws and intertial frames 4

1.3 The Galilean transformation 5

1.4 Newtonian relativity 6

1.5 Objections to absolute space; Mach's principle 7

1.6 The ether 9

1.7 Michelson and Morley's search for the ether 9

1.8 Lorentz's ether theory 10

1.9 Origins of special relativity 12

1.10 Further arguments for Einstein's two postulates 14

1.11 Cosmology and first doubts about inertial frames 15

1.12 Inertial and gravitational mass 16

1.13 Einstein's equivalence principle 18

1.14 Preview of general relativity 20

1.15 Caveats on the equivalence principle 22

1.16 Gravitational frequency shift and light bending 24

I Special Relativity 31

2 Foundations of special relativity; The Lorentz transformation 33

2.1 On the nature of physical theories 33

2.2 Basic features of special relativity 34

2.3 Relativistic problem solving 36

2.4 Relativity of simultaneity, time-dilation and length-contraction: a preview 38

2.5 The relativity principle and the homogeneity and isotropy of inertial frames 39

2.6 The coordinate lattice; Definitions of simultaneity 41

2.7 Derivation of the Lorentz transformation 43

2.8 Properties of the Lorentz transformation 47

2.9 Graphical representation of the Lorentz transformation 49

2.10 The relativistic speed limit 54

2.11 Which transformations are allowed by the relativity principle? 57

3 Relativistic kinematics 61

3.2 World-picture and world-map 61

3.3 Length contraction 62

3.4 Length contraction paradox 63

3.5 Time dilation; The twin paradox 64

3.6 Velocity transformation; Relative and mutual velocity 68

3.7 Acceleration transformation; Hyperbolic motion 70

3.8 Rigid motion and the uniformly accelerated rod 71

4 Relativistic optics 77

4.2 The drag effect 77

4.3 The Doppler effect 78

4.4 Aberration 81

4.5 The visual appearance of moving objects 82

5 Spacetime and four-vectors 89

5.1 The discovery of Minkowski space 89

5.2 Three-dimensional Minkowski diagrams 90

5.3 Light cones and intervals 91

5.4 Three-vectors 94

5.5 Four-vectors 97

5.6 The geometry of four-vectors 101

5.7 Plane waves 103

6 Relativistic particle mechanics 108

6.1 Domain of sufficient validity of Newtonian mechanics 108

6.2 The axioms of the new mechanics 109

6.3 The equivalence of mass and energy 111

6.4 Four-momentum identities 114

6.5 Relativistic billiards 115

6.6 The zero-momentum frame 117

6.7 Threshold energies 118

6.8 Light quanta and de Broglie waves 119

6.9 The Compton effect 121

6.10 Four-force and three-force 123

7 Four-tensors; Electromagnetism in vacuum 130

7.1 Tensors: Preliminary ideas and notations 130

7.2 Tensors: Definition and properties 132

7.3 Maxwell's equations in tensor form 139

7.4 The four-potential 143

7.5 Transformation of e and b; The dual field 146

7.6 The field of a uniformly moving point charge 148

7.7 The field of an infinite straight current 150

7.8 The energy tensor of the electromagnetic field 151

7.9 From the mechanics of the field to the mechanics of material continua 154

II General Relativity 163

8 Curved spaces and the basic ideas of general relativity 165

8.1 Curved surfaces 165

8.2 Curved spaces of higher dimensions 169

8.3 Riemannian spaces 172

8.4 A plan for general relativity 177

9 Static and stationary spacetimes 183

9.1 The coordinate lattice 183

9.2 Synchronization of clocks 184

9.3 First standard form of the metric 186

9.4 Newtonian support for the geodesic law of motion 188

9.5 Symmetries and the geometric characterization of static and stationary spacetimes 191

9.6 Canonical metric and relativistic potentials 195

9.7 The uniformly rotating lattice in Minkowski space 198

10 Geodesics, curvature tensor and vacuum field equations 203

10.1 Tensors for general relativity 203

10.2 Geodesics 204

10.3 Geodesic coordinates 208

10.4 Covariant and absolute differentiation 210

10.5 The Riemann curvature tensor 217

10.6 Einstein's vacuum field equations 221

11 The Schwarzschild metric 228

11.1 Derivation of the metric 228

11.2 Properties of the metric 230

11.3 The geometry of the Schwarzschild lattice 231

11.4 Contributions of the spatial curvature to post-Newtonian effects 233

11.5 Coordinates and measurements 235

11.6 The gravitational frequency shift 236

11.7 Isotropic metric and Shapiro time delay 237

11.8 Particle orbits in Schwarzschild space 238

11.9 The precession of Mercury's orbit 241

11.10 Photon orbits 245

11.11 Deflection of light by a spherical mass 248

11.12 Gravitational lenses 250

11.13 de Sitter precession via rotating coordinates 252

12 Black holes and Kruskal space 258

12.1 Schwarzschild black holes 258

12.2 Potential energy; A general-relativistic 'proof' of E = mc[superscript 2] 263

12.3 The extendibility of Schwarzschild spacetime 265

12.4 The uniformly accelerated lattice 267

12.5 Kruskal space 272

12.6 Black-hole thermodynamics and related topics 279

13 An exact plane gravitational wave 284

13.2 The plane-wave metric 284

13.3 When wave meets dust 287

13.4 Inertial coordinates behind the wave 288

13.5 When wave meets light 290

13.6 The Penrose topology 291

13.7 Solving the field equation 293

14 The full field equations; de Sitter space 296

14.1 The laws of physics in curved spacetime 296

14.2 At last, the full field equations 299

14.3 The cosmological constant 303

14.4 Modified Schwarzschild space 304

14.5 de Sitter space 306

14.6 Anti-de Sitter space 312

15 Linearized general relativity 318

15.1 The basic equations 318

15.2 Gravitational waves. The TT gauge 323

15.3 Some physics of plane waves 325

15.4 Generation and detection of gravitational waves 330

15.5 The electromagnetic analogy in linearized GR 335

III Cosmology 345

16 Cosmological spacetimes 347

16.2 Beginning to construct the model 358

16.3 Milne's model 360

16.4 The Friedman-Robertson-Walker metric 363

16.5 Robertson and Walker's theorem 368

17 Light propagation in FRW universes 373

17.1 Representation of FRW universes by subuniverses 373

17.2 The cosmological frequency shift 374

17.3 Cosmological horizons 376

17.4 The apparent horizon 382

17.5 Observables 384

18 Dynamics of FRW universes 391

18.1 Applying the field equations 391

18.2 What the field equations tell us 393

18.3 The Friedman models 396

18.4 Once again, comparison with observation 405

18.5 Inflation 409

18.6 The anthropic principle 413

Appendix Curvature tensor components for the diagonal metric 417.

Notes:

Includes bibliographical references and index.

ISBN:

0198508352

OCLC:

45505933