Preface |
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xiii | |
Notation, important formulae and physical constants |
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xiv | |
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1 | (17) |
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The Need for a theory of gravity |
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1 | (2) |
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Gravitation and inertia: the Equivalence Principle in mechanics |
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3 | (6) |
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The Equivalence Principle and optics |
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9 | (5) |
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14 | (2) |
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16 | (1) |
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16 | (2) |
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Special Relativity, non-inertial effects and electromagnetism |
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18 | (29) |
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Special Relativity: Einstein's train |
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18 | (8) |
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Twin paradox: accelerations |
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26 | (3) |
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Rotating frames: the Sagnac effect |
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29 | (5) |
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Inertia: Newton versus Mach |
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34 | (2) |
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36 | (4) |
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40 | (3) |
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Principle of General Covariance |
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43 | (2) |
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45 | (1) |
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46 | (1) |
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Differential geometry I: vectors, differential forms and absolute differentiation |
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47 | (65) |
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Space-time as a differentiable manifold |
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47 | (2) |
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Vectors and vector fields |
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49 | (6) |
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55 | (6) |
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61 | (4) |
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Differential forms: Hodge duality |
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65 | (7) |
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Exterior derivative operator: generalised Stokes' theorem |
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72 | (5) |
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Maxwell's equations and differential forms |
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77 | (2) |
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79 | (7) |
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Absolute differentiation: connection forms |
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86 | (7) |
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93 | (4) |
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Some relations involving connection coefficients |
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97 | (5) |
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102 | (5) |
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General formula for connection coefficients |
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107 | (3) |
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110 | (1) |
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110 | (2) |
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Differential geometry II: geodesics and curvature |
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112 | (25) |
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Autoparallel curves and geodesics |
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112 | (7) |
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119 | (2) |
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121 | (4) |
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Symmetries of the Riemann tensor |
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125 | (1) |
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Ricci tensor and curvature scalar |
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126 | (3) |
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129 | (3) |
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132 | (2) |
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134 | (1) |
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135 | (1) |
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135 | (2) |
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Einstein field equations, the Schwarzschild solution and experimental tests of General Relativity |
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137 | (43) |
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137 | (2) |
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139 | (7) |
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146 | (5) |
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Time dependence and spherical symmetry: Birkhoff's theorem |
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151 | (3) |
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154 | (4) |
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Geodesics in Schwarzschild space-time |
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158 | (2) |
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Precession of planetary orbits |
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160 | (2) |
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162 | (2) |
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164 | (1) |
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165 | (4) |
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Radar echoes from planets |
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169 | (4) |
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Radial motion in a Schwarzschild field: black holes - frozen stars |
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173 | (3) |
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A gravitational clock effect |
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176 | (2) |
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178 | (1) |
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178 | (2) |
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Gravitomagnetic effects: gyroscopes and clocks |
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180 | (47) |
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180 | (11) |
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Precession of gyroscopes: the Lense-Thirring effect |
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191 | (9) |
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200 | (4) |
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Gravitomagnetic clock effect |
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204 | (3) |
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Fermi---Walker transport: tetrad formalism |
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207 | (4) |
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Lie derivatives, Killing vectors and groups of motion |
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211 | (8) |
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Static and stationary space-times |
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219 | (4) |
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Killing vectors and conservation laws |
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223 | (2) |
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225 | (1) |
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226 | (1) |
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Gravitational collapse and black holes |
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227 | (68) |
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The interior Schwarzschild solution and the Tolman---Oppenheimer-Volkoff equation |
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228 | (9) |
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Energy density and binding energy |
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237 | (6) |
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Degenerate stars: white dwarfs and neutron stars |
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243 | (8) |
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Schwarzschild orbits: Eddington-Finkelstein coordinates |
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251 | (4) |
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Kruskal-Szekeres coordinates |
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255 | (4) |
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Einstein-Rosen bridge and wormholes |
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259 | (2) |
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Conformal treatment of infinity: Penrose diagrams |
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261 | (4) |
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Rotating black holes: Kerr solution |
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265 | (6) |
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The ergosphere and energy extraction from a black hole |
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271 | (9) |
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280 | (7) |
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Thermodynamics of black holes and further observations |
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287 | (4) |
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Global matters: singularities, trapped surfaces and Cosmic Censorship |
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291 | (2) |
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293 | (1) |
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294 | (1) |
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Action principle, conservation laws and the Cauchy problem |
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295 | (15) |
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Gravitational action and field equations |
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295 | (5) |
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Energy-momentum pseudotensor |
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300 | (4) |
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304 | (5) |
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309 | (1) |
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309 | (1) |
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310 | (31) |
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310 | (7) |
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Radiation from a rotating binary source |
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317 | (11) |
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Parallels between electrodynamics and General Relativity: Petrov classification |
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328 | (12) |
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340 | (1) |
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340 | (1) |
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341 | (51) |
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Brief description of the Universe |
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341 | (3) |
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344 | (11) |
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Hubble's law and the cosmological red-shift |
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355 | (2) |
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357 | (3) |
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Luminosity-red-shift relation |
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360 | (3) |
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Dynamical equations of cosmology |
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363 | (8) |
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Friedmann models and the cosmological constant |
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371 | (4) |
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Cosmic background radiation |
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375 | (2) |
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Brief sketch of the early Universe |
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377 | (6) |
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The inflationary universe and the Higgs mechanism |
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383 | (8) |
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391 | (1) |
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391 | (1) |
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Gravitation and field theory |
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392 | (33) |
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Electrodynamics as an abelian gauge theory |
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394 | (6) |
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Non-abelian gauge theories |
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400 | (9) |
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Gauging Lorentz symmetry: torsion |
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409 | (7) |
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Dirac equation in Schwarzschild space-time |
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416 | (2) |
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Five dimensions: gravity plus electromagnetism |
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418 | (5) |
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423 | (1) |
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424 | (1) |
References |
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425 | (14) |
Index |
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439 | |