| Preface |
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vii | |
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1 Basics of geometry and relativity |
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1 | (34) |
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1.1 Two dimensional geometry |
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1 | (12) |
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1.2 Inertial and gravitational masses |
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13 | (3) |
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16 | (19) |
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35 | (30) |
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2.1 Relativistic point particle |
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35 | (11) |
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2.2 Current and charge densities |
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46 | (5) |
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2.3 Maxwell's equations in the presence of sources |
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51 | (3) |
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2.4 Motion of a charged particle in EM field |
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54 | (2) |
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2.5 Energy-momentum tensor |
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56 | (5) |
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61 | (4) |
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3 Principle of general covariance |
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65 | (18) |
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3.1 Principle of equivalence |
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65 | (5) |
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3.2 Principle of general covariance |
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70 | (6) |
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76 | (7) |
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4 Affine connection and covariant derivative |
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83 | (50) |
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4.1 Parallel transport of a vector |
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83 | (13) |
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96 | (9) |
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4.3 Covariant derivative of contravariant tensors |
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105 | (6) |
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111 | (4) |
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4.5 Covariant derivative of covariant and mixed tensors |
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115 | (3) |
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4.6 Electromagnetic analogy |
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118 | (2) |
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4.7 Gradient, divergence and curl |
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120 | (13) |
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133 | (34) |
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5.1 Covariant differentiation along a curve |
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133 | (2) |
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5.2 Curvature from derivatives |
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135 | (4) |
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5.3 Parallel transport along a closed curve |
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139 | (10) |
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149 | (12) |
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5.5 Derivation of geodesic equation from a Lagrangian |
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161 | (6) |
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6 Applications of the geodesic equation |
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167 | (32) |
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6.1 Geodesic as representing gravitational effect |
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167 | (5) |
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6.2 Rotating coordinate system and the Coriolis force |
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172 | (8) |
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6.3 Gravitational red shift |
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180 | (10) |
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6.4 Twin paradox and general covariance |
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190 | (3) |
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6.5 Other equations in the presence of gravitation |
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193 | (6) |
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7 Curvature tensor and Einstein's equation |
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199 | (38) |
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7.1 Curvilinear coordinates versus gravitational field |
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199 | (1) |
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7.2 Definition of an inertial coordinate frame |
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199 | (1) |
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200 | (3) |
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7.4 Properties of the curvature tensor |
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203 | (11) |
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214 | (8) |
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7.6 Cosmological constant |
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222 | (1) |
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7.7 Initial value problem |
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223 | (6) |
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7.8 Einstein's equation from an action |
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229 | (8) |
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237 | (28) |
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237 | (3) |
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240 | (4) |
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8.3 Solution of the Einstein equation |
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244 | (13) |
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8.4 Properties of the Schwarzschild solution |
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257 | (3) |
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8.5 Isotropic coordinates |
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260 | (5) |
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9 Tests of general relativity |
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265 | (30) |
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9.1 Radar echo experiment |
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265 | (2) |
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9.2 Motion of a particle in a Schwarzschild background |
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267 | (13) |
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273 | (4) |
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277 | (3) |
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9.3 Motion of light rays in a Schwarzschild background |
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280 | (7) |
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9.4 Perihelion advance of Mercury |
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287 | (8) |
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295 | (16) |
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10.1 Singularities of the metric |
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296 | (5) |
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10.2 Singularities of the Schwarzschild metric |
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301 | (5) |
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306 | (5) |
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11 Cosmological models and the big bang theory |
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311 | (24) |
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11.1 Homogeneity and isotropy |
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311 | (3) |
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11.2 Different models of the universe |
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314 | (2) |
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314 | (1) |
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315 | (1) |
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315 | (1) |
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316 | (4) |
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320 | (9) |
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325 | (2) |
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327 | (1) |
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328 | (1) |
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11.5 Big bang theory and blackbody radiation |
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329 | (6) |
| Index |
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335 | |
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