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Relativity, Gravitation, and Cosmology: A Basic Introduction
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Title: Relativity, Gravitation, and Cosmology: A Basic Introduction (Oxford Master Series in Physics) Author(s): Ta-Pei Cheng Publisher: Year: 2005 Language: English Einstein's general theory of relativity is introduced in this advanced undergraduate and beginning graduate level textbook. Topics include special relativity in the formalism of Minkowski's four-dimensional space-time, the principle of equivalence, Riemannian geometry and tensor analysis, Einstein's field equation and cosmology. The author presents the subject from the very beginning with an emphasis on physical examples and simple applications without the full tensor apparatus. One first learns how to describe curved spacetime. At this mathematically more accessible level, the reader can already study the many interesting phenomena such as gravitational lensing, precession of Mercury's perihelion, black holes, as well as cosmology. The full tensor formulation is presented later, when the Einstein equation is solved for a few symmetric cases. Many modern topics in cosmology are discussed in this book: from inflation and cosmic microwave anisotropy to the "dark energy" that propels as accelerating universe. Mathematical accessibility, together with the various pedagogical devices (e.g., worked-out solutions of chapter-end problems), make it practical for interested readers to use the book to study general relativity, gravitation and cosmology on their own. Table of contents : Contents......Page 10 Part I: RELATIVITY: Metric Description of Spacetime......Page 16 1 Introduction and overview......Page 18 1.1 Relativity as a coordinate symmetry......Page 20 1.2 GR as a gravitational field theory......Page 23 Review questions......Page 27 2.1 Coordinate symmetries......Page 29 2.2 The new kinematics of space and time......Page 34 2.3 Geometric formulation of SR......Page 39 Problems......Page 50 3.1 Newtonian gravitation potential—a review......Page 53 3.2 EP introduced......Page 54 3.3 Implications of the strong EP......Page 58 Problems......Page 68 4 Metric description of a curved space......Page 70 4.1 Gaussian coordinates......Page 71 4.2 Metric tensor......Page 72 4.3 Curvature......Page 78 Review questions......Page 83 Problems......Page 84 5.1 Geometry as gravity......Page 86 5.2 Geodesic equation as GR equation of motion......Page 90 5.3 The curvature of spacetime......Page 94 Problems......Page 100 6.1 Description of Schwarzschild spacetime......Page 102 6.2 Gravitational lensing......Page 107 6.3 Precession of Mercury's perihelion......Page 112 6.4 Black holes......Page 117 Review questions......Page 126 Problems......Page 127 Part II: COSMOLOGY......Page 128 7 The homogeneous and isotropic universe......Page 130 7.1 The cosmos observed......Page 131 7.2 The cosmological principle......Page 140 7.3 The Robertson–Walker metric......Page 142 Review questions......Page 148 Problems......Page 149 8 The expanding universe and thermal relics......Page 151 8.1 Friedmann equations......Page 152 8.2 Time evolution of model universes......Page 157 8.3 Big bang cosmology......Page 160 8.4 Primordial nucleosynthesis......Page 164 8.5 Photon decoupling and the CMB......Page 167 Review questions......Page 177 Problems......Page 178 9 Inflation and the accelerating universe......Page 180 9.1 The cosmological constant......Page 181 9.2 The inflationary epoch......Page 185 9.3 CMB anisotropy and evidence for k = 0......Page 193 9.4 The accelerating universe in the present epoch......Page 198 9.5 The concordant picture......Page 204 Problems......Page 208 Part III: RELATIVITY: Full Tensor Formulation......Page 210 10.1 General coordinate systems......Page 212 10.2 Four-vectors in Minkowski spacetime......Page 215 10.3 Manifestly covariant formalism for E&M......Page 220 10.4 Energy–momentum tensors......Page 223 Problems......Page 228 11.1 Derivatives in a curved space......Page 230 11.2 Parallel transport......Page 237 11.3 Riemannian curvature tensor......Page 240 Review questions......Page 245 Problems......Page 246 12.1 The principle of general covariance......Page 248 12.2 Einstein field equation......Page 251 12.3 The Schwarzschild exterior solution......Page 254 12.4 The Einstein equation for cosmology......Page 259 Problems......Page 263 13 Linearized theory and gravitational waves......Page 265 13.1 The linearized Einstein theory......Page 266 13.2 Plane waves and the polarization tensor......Page 269 13.3 Gravitational wave detection......Page 270 13.4 Evidence for gravitational wave......Page 274 Review questions......Page 283 Problems......Page 284 A.1 The twin paradox (Section 2.3.4)......Page 286 A.2 A glimpse of advanced topics in black hole physics (Section 6.4)......Page 290 A.3 False vacuum and hidden symmetry (Section 9.2.2)......Page 294 A.4 The problem of quantum vacuum energy as Λ (Section 9.4)......Page 295 B: Answer keys to review questions......Page 298 C: Solutions of selected problems......Page 308 References......Page 345 Bibliography......Page 348 C......Page 350 G......Page 351 L......Page 352 P......Page 353 T......Page 354 Z......Page 355 |
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