广义相对论基础教程 原书第2版PDF|Epub|txt|kindle电子书版本网盘下载

广义相对论基础教程 原书第2版PDF格式电子书版下载

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1 Special relativity1

1.1 Fundamental principles of special relativity（SR）theory1

1.2 Definition of an inertial observer in SR3

1.3 New units4

1.4 Spacetime diagrams5

1.5 Construction of the coordinates used by another observer6

1.6 Invariance of the interval9

1.7 Invariant hyperbolae14

1.8 Particularly important results17

1.9 The Lorentz transformation21

1.10 The velocity-composition law22

1.11 Paradoxes and physical intuition23

1.12 Further reading24

1.13 Appendix：The twin ‘paradox’dissected25

1.14 Exercises28

2 Vector analysis in special relativity33

2.1 Definition of a vector33

2.2 Vector algebra36

2.3 The four-velocity41

2.4 The four-momentum42

2.5 Scalar product44

2.6 Applications46

2.7 Photons49

2.8 Further reading50

2.9 Exercises50

3 Tensor analysis in special relativity56

3.1 The metric tensor56

3.2 Definition of tensors56

3.3 The（0 1）tensors：one-forms58

3.4 The（0 2）tensors66

3.5 Metric as a mapping of vectors into one-forms68

3.6 Finally：（M N）tensors72

3.7 Index ‘raising’and ‘lowering’74

3.8 Differentiation of tensors76

3.9 Further reading77

3.10 Exercises77

4 Perfect fluids in special relativity84

4.1 Fluids84

4.2 Dust：the number-flux vector →N85

4.3 One-forms and surfaces88

4.4 Dust again：the stress-energy tensor91

4.5 General fluids93

4.6 Perfect fluids100

4.7 Importance for general relativity104

4.8 Gauss’law105

4.9 Further reading106

4.10 Exercises107

5 Preface to curvature111

5.1 On the relation of gravitation to curvature111

5.2 Tensor algebra in polar coordinates118

5.3 Tensor calculus in polar coordinates125

5.4 Christoffel symbols and the metric131

5.5 Noncoordinate bases135

5.6 Looking ahead138

5.7 Further reading139

5.8 Exercises139

6 Curved manifolds142

6.1 Differentiable manifolds and tensors142

6.2 Riemannian manifolds144

6.3 Covariant differentiation150

6.4 Parallel-transport，geodesics，and curvature153

6.5 The curvature tensor157

6.6 Bianchi identities：Ricci and Einstein tensors163

6.7 Curvature in perspective165

6.8 Further reading166

6.9 Exercises166

7 Physics in a curved spacetime171

7.1 The transition from differential geometry to gravity171

7.2 Physics in slightly curved spacetimes175

7.3 Curved intuition177

7.4 Conserved quantities178

7.5 Further reading181

7.6 Exercises181

8 The Einstein field equations184

8.1 Purpose and justification of the field equations184

8.2 Einstein’s equations187

8.3 Einstein’s equations for weak gravitational fields189

8.4 Newtonian gravitational fields194

8.5 Further reading197

8.6 Exercises198

9 Gravitational radiation203

9.1 The propagation of gravitational waves203

9.2 The detection of gravitational waves213

9.3 The generation of gravitational waves227

9.4 The energy carried away by gravitational waves234

9.5 Astrophysical sources of gravitational waves242

9.6 Further reading247

9.7 Exercises248

10 Spherical solutions for stars256

10.1 Coordinates for spherically symmetric spacetimes256

10.2 Static spherically symmetric spacetimes258

10.3 Static perfect fluid Einstein equations260

10.4 The exterior geometry262

10.5 The interior structure of the star263

10.6 Exact interior solutions266

10.7 Realistic stars and gravitational collapse269

10.8 Further reading276

10.9 Exercises277

11 Schwarzschild geometry and black holes281

11.1 Trajectories in the Schwarzschild spacetime281

11.2 Nature of the surface r ＝ 2M298

11.3 General black holes304

11.4 Real black holes in astronomy318

11.5 Quantum mechanical emission of radiation by black holes：the Hawking process323

11.6 Further reading327

11.7 Exercises328

12 Cosmology335

12.1 What is cosmology？335

12.2 Cosmological kinematics：observing the expanding universe337

12.3 Cosmological dynamics：understanding the expanding universe353

12.4 Physical cosmology：the evolution of the universe we observe361

12.5 Further reading369

12.6 Exercises370

Appendix A Summary of linear algebra374

References378

Index386