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Relativity: modern large-scale spacetime structure of the cosmos

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Bibliographische Detailangaben
Format:	Buch
Sprache:	English
Veröffentlicht:	Singapore [u.a.] World Scientific 2008
Schlagworte:	Cosmologie Espace et temps Relativité restreinte (Physique) Cosmology Space and time Special relativity (Physics) Kosmologie Allgemeine Relativitätstheorie Spezielle Relativitätstheorie Cosmology. Space and time.
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Includes bibliographical references (p. 421-502) and index
Beschreibung:	XXV, 524 S. graph. Darst.
ISBN:	9789812813756

Internformat

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Datensatz im Suchindex

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adam_text	Contents Acknowledgements vii Foreword ix Preface xiii 1. Special Relativity Theory, by Moshe Carmeli 1 1.1 Spacetime in Four Dimensions .............. 2 1.1.1 Postulates of special relativity .......... 2 1.1.2 The principle of relativity: Constancy of the speed of light ................... 2 1.1.3 Coordinates and the line element ........ 5 1.1.4 Inerţial coordinate system ............ 5 1.1.5 Simultaneity .................... 5 1.1.6 The Galilean transformation ........... 6 1.1.7 Difficulties with light ............... 6 1.1.8 Role of velocity in classical physics ....... 8 1.1.9 The Galilean group ................ 8 1.2 The Lorentz Transformation ................ 9 1.2.1 Measuring rods and clocks ............ 9 1.2.2 Spatial coordinates and time ........... 9 1.2.3 Einstein s paradox ................ 9 1.2.4 Apparent incompatibility of the special relativity postulates ................ 10 1.2.5 Derivation of the Lorentz transformation .... 11 1.3 The Light Cone ....................... 17 1.3.1 Events and coordinate systems ......... 17 vi Relativity: Modern Large-Scale Spaceüme Structure of the Cosmos 1.3.2 Future and past .................. 19 1.3.3 Problems ...................... 19 1.4 The Lorentz Group ..................... 20 1.4.1 Problems ...................... 21 1.5 Consequences of the Lorentz Transformation ...... 25 1.5.1 Nonrelativistic limit ................ 26 1.5.2 The Lorentz contraction of lengths ....... 26 1.5.3 The dilation of time ............... 26 1.5.4 The addition of velocities law .......... 27 1.5.5 Problems ...................... 28 1.6 The Structure of Spacetime ................ 30 1.6.1 Special relativity as a valuable guide ...... 32 l.C. 2 Four dimensions in classical mechanics ..... 33 1.6.3 The Minkowskian spacetime ........... 33 1.6.4 The proper time .................. 36 1.6.5 Velocity and acceleration four-vectors ...... 38 1.6.6 Problems ...................... 40 1.7 Mass, Energy and Momentum ............... 40 1.7.1 Preliminaries ................... 40 1.7.2 Relationship between mass, energy and momentum .................. 41 1.7.3 Angular-momentum representation ....... 44 1.7.4 Energy-momentum four-vector .......... 46 1.7.5 Problems ...................... 47 1.8 Suggested References .................... 48 2. Cosmological Special Relativity, by Moshe Carmeli 51 2.1 Spacevelocity in Four Dimensions ............. 52 2.1.1 Present-day cosmology .............. 53 2.1.2 Postulates ..................... 53 2.1.3 The cosmic frames ................ 53 2.1.4 Spacevelocity in cosmology ............ 54 2.1.5 Pre-special relativity ............... 55 2.1.6 The relative cosmic time ............. 55 2.1.7 Inadequacy of the classical transformation ... 56 2.1.8 Nonrelativistic cosmological transformation . . 56 2.1.9 Difficulties at the Big Bang ........... 57 2.1.10 Universe expansion versus light propagation . . 58 2.2 The Cosmological Transformation ............ 59 Contents xvii 2.2.1 Problems...................... 60 2.3 The Galaxy Cone...................... 61 2.4 Consequences of the Cosmological Transformation ... 63 2.4.1 The classical limit ................. 63 2.4.2 The length contraction .............. 63 2.4.3 The velocity contraction ............. 64 2.4.4 The law of addition of cosmic times ....... 65 2.4.5 The inflation of the Universe ........... 66 2.4.6 Minimal acceleration in the expansion of the Universe .................. 67 2.4.7 The cosmological redshift ............ 67 2.4.8 The temperature of the Universe ........ 67 2.4.9 The relationship between redshift and cosmic time .................... 69 2.4.10 Problems ...................... 71 2.5 Velocity, Acceleration and Cosmic Distances ....... 73 2.5.1 Preliminaries ................... 73 2.5.2 Velocity and acceleration four-vectors ...... 73 2.5.3 Acceleration and distances ............ 75 2.5.4 Energy in ESR versus cosmic distance in CSR ....................... 76 2.5.5 Distance-velocity four-vector ........... 77 2.5.6 Conclusions .................... 78 2.6 Suggested References .................... 79 3. General Relativity Theory, by Moshe Carmeli 83 3.1 Riemannian Geometry ................... 84 3.1.1 Transformation of coordinates .......... 84 3.1.2 Contravariant vectors ............... 85 3.1.3 Invariants. Covariant vectors .......... 85 3.1.4 Tensors ....................... 86 3.1.5 The metric tensor ................. 86 3.1.6 The Christoffel symbols ............. 87 3.1.7 Covariant differentiation ............. 90 3.1.8 The Riemann, Ricci and Einstein tensors .... 91 3.1.9 Geodesies ..................... 95 3.1.10 The Bianchi identities .............. 97 3.1.11 Tensor densities .................. 97 3.1.12 Problems ...................... 101 Relativity: Modern Large-Scale Spaceüme Structure of the Cosmos 3.2 The Principle of Equivalence ............... 116 3.2.1 Null experiments: Eötvös experiment ...... 116 3.3 The Principle of General Covariance ........... 118 3.4 Gravitational Field Equations ............... 119 3.4.1 The Einstein field equations ........... 119 3.4.2 Problems ...................... 120 3.4.3 The Newtonian limit in general relativity .... 125 3.4.4 Derivation of the Einstein equations from variational principle ................ 130 3.4.5 The electromagnetic energy-momentum tensor ....................... 131 3.5 The Schwarzschild Solution ................ 131 3.6 Experimental Tests of General Relativity ........ 139 3.6.1 The gravitational redshift ............ 139 3.6.2 Effects on planetary motion ........... 140 3.6.3 The deflection of light .............. 143 3.6.4 Gravitational radiation experiments ....... 145 3.6.5 Radar experiment ................. 146 3.6.6 Low-temperature experiments .......... 147 3.7 Equations of Motion .................... 147 3.7.1 The geodesic postulate .............. 147 3.7.2 Equations of motion as a consequence of field equations ................... 148 3.7.3 Self-action terms ................. 149 3.7.4 The Einstein-Infeld-Hoffmann method ..... 152 3.7.5 The Newtonian equation of motion ....... 154 3.7.6 The Einstein-Infeld-Hoffmann equation ..... 154 3.8 Decomposition of the Riemann Tensor .......... 156 3.9 Problems .......................... 156 3.10 Suggested References .................... 159 Cosmological General Relativity, by Moshe Carmeli 161 4.1 Cosmology in Spacevelocity ................ 162 4.1.1 The foundations of CGR ............. 162 4.1.2 The null condition ds = 0............ 163 4.1.3 Gravitational field equations ........... 163 4.1.4 The energy-momentum tensor .......... 163 4.1.5 The Newtonian limit in cosmological general relativity ................. 164 Contents xix 4.1.6 Spherically-symmetric vacuum solution of the Einstein field equations in CGR ......... 170 4.2 Spherically-Symmetric Metric ............... 175 4.2.1 Energy-momentum tensor with pressure .... 175 4.2.2 The metric ..................... 176 4.2.3 The field equations ................ 176 4.2.4 Solutions ...................... 177 4.2.5 The Universe expansion ............. 179 4.2.6 Problem (a) .................... 180 4.2.7 Integration of equation of motion ........ 180 4.2.8 Physical meaning ................. 182 4.2.9 Expansion at present epoch of time ....... 183 4.2.10 Problem (b) .................... 185 4.2.11 The value of the constant r ........... 185 4.3 Tolman Metric as an Expanding Universe ........ 186 4.3.1 The Tolman metric ................ 186 4.3.2 Field equations .................. 188 4.3.3 Solutions ...................... 189 4.3.4 The Universe expansion ............. 190 4.3.5 Tolman s Universe with pressure ........ 191 4.3.6 Problem ...................... 193 4.4 Kantowski-Sachs Metrics as Expanding Universes .... 194 4.4.1 Introduction .................... 194 4.4.2 Coordinate system ................ 194 4.4.3 The group generators ............... 194 4.4.4 The field equations ................ 195 4.4.5 Solutions of the field equations ......... 196 4.4.6 Kantowski-Sachs metrics in space-velocity manifold of cosmological general relativity ... 198 4.4.7 Problems ...................... 199 4.5 Gravitational Lensing in an Expanding Universe .... 202 4.5.1 Introduction .................... 202 4.5.2 Equation of motion of light in the Tolman expanding Universe ................ 203 4.5.3 Light propagation in the lowest approximation . 206 4.5.4 The second approximation ............ 206 4.5.5 The contribution due to the expansion ..... 208 4.6 Suggested References .................... 208 кх Relativity: Modern Large-Scale Spacetime Structure of the Cosmos 5. Properties of the Gravitational Field, by Moshe Carmeli 211 5.1 The Newtonian Equation of Motion ........... 211 5.1.1 The Newtonian limit of the Einstein field equations ..................... 212 5.1.2 The Newtonian potential ............. 212 5.1.3 The lowest approximation ............ 213 5.1.4 The function ф(х) ................. 214 5.2 The Geodesic Equation in Cosmology .......... 215 5.2.1 Problem ...................... 217 5.3 The Dynamics of the Universe Expansion: Analogy with Newtonian Mechanics ................... 219 5.3.1 Acceleration in cosmology ........... 220 5.3.2 The acceleration term explicitly: Determining the type of the Universe ............. 221 5.4 Hook s Law of the Universe ................ 222 5.5 Suggested References .................... 223 6. Cosmological Special Relativity in Five Dimensions, by Moshe Carmeli 225 6.1 Introduction ......................... 225 6.2 Some Consequences of the Extension to Five Dimensions ......................... 226 6.3 Generalized Maxwell s Equations ............. 228 6.3.1 The mix-up .................... 229 6.4 Concluding Remarks .................... 230 6.5 Suggested References .................... 231 7. Cosmological General Relativity in Five Dimensions: Brane World Theory, by Moshe Carmeli 233 7.1 Introduction ......................... 233 7.1.1 Five-dimensional manifold of space, time and velocity .................... 234 7.2 Universe with Gravitation ................. 234 7.2.1 The Bianchi identities .............. 235 7.2.2 The gravitational field equations ........ 235 7.2.3 The velocity as an independent coordinate . . . 236 7.2.4 Effective mass density in cosmology ....... 236 7.3 The Accelerating Universe ................. 237 Contents xxi 7.3.1 Preliminaries ................... 237 7.3.2 Expanding Universe ............... 238 7.3.3 Decelerating, constant and accelerating expansions ..................... 240 7.3.4 The accelerating Universe ............ 241 7.4 The Tully-Fisher Formula: Nonexistence of Halo Dark Matter ............................ 242 7.4.1 The geodesic equation .............. 243 7.4.2 The equations of motion ............. 244 7.4.3 The Tully-Fisher law ............... 246 7.5 Cosmological Redshift Analysis .............. 247 7.5.1 The redshift formula ............... 247 7.5.2 Particular cases .................. 248 7.5.3 Conclusions .................... 249 7.6 Verification of the classical general relativity tests in the Five-Dimensional Cosmology ............... 250 7.6.1 Comparison with general relativity ....... 250 7.6.2 Problem ...................... 252 7.6.3 The gravitational redshift in five dimensions . . 253 7.6.4 Motion in a centrally symmetric gravitational field in cosmological five dimensions ....... 254 7.6.5 The deflection of light in a gravitational field within the five-dimensional theory ........ 259 7.7 Suggested References .................... 262 8. Particle Production in Five-Dimensional Cosmological Relativity, by Gianluca Gemelli 265 8.1 Introduction ......................... 265 8.2 Relativistic Hydrodynamics ................ 266 8.3 Five-Dimensional Relativity ................ 268 8.4 Particle Production ..................... 270 8.5 5D Hydrodynamics ..................... 272 8.6 The Isentropic Case .................... 274 8.7 Simulation of Friedmann Cosmology in Flat Spacetime . 275 8.8 Suggested References .................... 280 9. Properties of Gravitational Waves in an Expanding Universe, by John Hartnett & Michael Tobar 283 xxii Relativity: Modem Large-Scale Spacetime Structure of the Cosmos 9.1 Introduction ......................... 283 9.1.1 Cosmological general relativity — A brief review ....................... 284 9.1.2 Linearized gravitational field equations ..... 284 9.2 Wave Equation in Curved Spacevelocity ......... 286 9.2.1 Plane wave solution ................ 287 9.2.2 Solutions of the field equations ......... 288 9.2.3 Phase and group velocities ............ 289 9.3 Density Scales in the Universe ............... 291 9.3.1 The case of binary pulsar ............ 292 9.4 Conclusion ......................... 292 9.5 Problems .......................... 293 9.6 Suggested References .................... 294 10. Spiral Galaxy Rotation Curves in the Brane World Theory in Five Dimensions, by John Hartnett 297 10.1 Introduction ......................... 297 10.2 Gravitational Potential ................... 299 10.3 Equations of Motion .................... 300 10.3.1 Newtonian ..................... 300 10.3.2 Carmelian ..................... 301 10.3.3 Rotation curves .................. 303 10.4 Accelerations ........................ 305 10.5 Sample of Galaxy Rotation Curves ............ 307 10.5.1 Extragalactic spirals ............... 308 10.5.2 The galaxy ..................... 313 10.6 Conclusion ......................... 315 10.7 Suggested References .................... 315 11. The Friedmann Universe: FRW Metric, by Moshe Carmeli 319 11.1 Introduction ......................... 319 11.1.1 Some preliminary concepts ............ 322 11.2 The Geometry of the Three-Dimensional Homogeneous and Isotropie Space ............ 323 11.2.1 Choice of coordinate system ........... 324 11.2.2 Space with constant positive curvature ..... 325 11.2.3 Space with constant negative curvature ..... 326 11.2.4 Space with zero curvature ............ 326 Contents xxiii 11.2.5 Problems...................... 326 11.3 The Friedmann Model................... 327 11.3.1 Space with positive curvature .......... 328 11.3.2 Remark I ..................... 330 11.3.3 Space with negative curvature.......... 330 11.3.4 Remark 2..................... 331 11.3.5 Space with zero curvature ............ 331 11.3.6 Problems ...................... 331 11.4 Propagation of Light in the Friedmann Model ...... 332 11.4.1 Problems ...................... 333 11.5 FRW Metric ........................ 334 11.5.1 Remarks on the critical mass density pc .... 336 116 Suggested References .................... 336 12. CGR versus FRW, by Moshe Carmeli 337 12.1 The Cosmic Time as a Relative Quantity ........ 337 12.1.1 The line element in empty space ......... 338 12.1.2 The line element with gravity .......... 340 12.2 Suggested References .................... 341 13. Testing CGR against High Redshift Observations, by John Hartnett & Firmin Oliveira 343 13.1 Introduction ......................... 343 13.2 Luminosity Distance .................... 344 13.3 Angular Size ........................ 345 13.4 Surface Brightness ..................... 348 13.5 Matter Density of the Universe .............. 348 13.6 Expansion Transition Redshift zt ............. 350 13.7 Comparison with High-Z Type la Supernovae Data . . . 350 13.7.1 Quality of curve fits ................ 351 13.8 Values of Some Key Parameters .............. 356 13.8.1 Hubble constant .................. 356 13.8.2 Mass of the Universe ............... 356 13.8.3 Time of transition from deceleration to acceleration .................... 357 13.9 Conclusion ......................... 359 13.10 Approximation of Ω .................... 359 13.11 Suggested References .................... 360 xxiv Relativity: Modern Large-Scale Spacetime Structure of the Cosmos 14. Extending the Hubble Diagram to Higher Redshifts in CGR, by John Hartnett 363 14.1 Introduction ......................... 363 14.1.1 Spacevelocity equations .............. 364 14.2 Comparison with Observation ............... 365 14.2.1 Extended redshift range ............. 367 14.2.2 Quality of curve fits ................ 370 14.3 Spatially Flat Universe ................... 375 14.4 Conclusion ......................... 378 14.5 Suggested References .................... 379 15. Homogeneous Spaces and Bianchi Classification, by Moshe Carmeli 381 15.1 Lie Derivative ........................ 381 15.1.1 Infinitesimal transformation ........... 383 15.1.2 Problems ...................... 386 15.2 The Killing Equation .................... 391 15.2.1 Isometric mapping ................ 391 15.2.2 Killing equation. Killing vector ......... 392 15.2.3 Example: The Poincaré group .......... 393 15.2.4 Problems ...................... 398 15.3 Bianchi Types ....................... 402 15.4 Suggested References .................... 402 Appendix A Mathematical Conventions 405 A.I Components of the Ricci tensor .............. 406 Appendix В Integration of the Equation of the Universe Expansion 407 Appendix С Spheroidal and Elliptical Galaxy Velocity Dispersion from CGR 409 C.I Introduction ......................... 409 C.2 Gravitational Potential ................... 410 C.3 Equations of Motion .................... 411 C.3.1 Newtonian ..................... 411 C.3.2 Carmelian ..................... 412 C.4 Radial Velocity Dispersion ................. 414 Contents xxv C.4.1 Newtonian..................... 414 C.4.2 Carmelian..................... 415 C.4.3 Discussion ..................... 416 С. 5 Conclusion ......................... 419 С. 6 Suggested References .................... 420 Appendix D Bibliography 421 Index 503
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publisher	World Scientific
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spelling	Relativity modern large-scale spacetime structure of the cosmos ed. Moshe Carmeli Singapore [u.a.] World Scientific 2008 XXV, 524 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 421-502) and index Cosmologie Espace et temps Relativité restreinte (Physique) Cosmology Space and time Special relativity (Physics) Kosmologie (DE-588)4114294-9 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Spezielle Relativitätstheorie (DE-588)4182215-8 gnd rswk-swf Cosmology. Space and time. Allgemeine Relativitätstheorie (DE-588)4112491-1 s DE-604 Spezielle Relativitätstheorie (DE-588)4182215-8 s Kosmologie (DE-588)4114294-9 s Carmeli, Moshe 1933-2007 Sonstige (DE-588)128455624 oth Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018623605&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Relativity modern large-scale spacetime structure of the cosmos Cosmologie Espace et temps Relativité restreinte (Physique) Cosmology Space and time Special relativity (Physics) Kosmologie (DE-588)4114294-9 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Spezielle Relativitätstheorie (DE-588)4182215-8 gnd
subject_GND	(DE-588)4114294-9 (DE-588)4112491-1 (DE-588)4182215-8
title	Relativity modern large-scale spacetime structure of the cosmos
title_auth	Relativity modern large-scale spacetime structure of the cosmos
title_exact_search	Relativity modern large-scale spacetime structure of the cosmos
title_full	Relativity modern large-scale spacetime structure of the cosmos ed. Moshe Carmeli
title_fullStr	Relativity modern large-scale spacetime structure of the cosmos ed. Moshe Carmeli
title_full_unstemmed	Relativity modern large-scale spacetime structure of the cosmos ed. Moshe Carmeli
title_short	Relativity
title_sort	relativity modern large scale spacetime structure of the cosmos
title_sub	modern large-scale spacetime structure of the cosmos
topic	Cosmologie Espace et temps Relativité restreinte (Physique) Cosmology Space and time Special relativity (Physics) Kosmologie (DE-588)4114294-9 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Spezielle Relativitätstheorie (DE-588)4182215-8 gnd
topic_facet	Cosmologie Espace et temps Relativité restreinte (Physique) Cosmology Space and time Special relativity (Physics) Kosmologie Allgemeine Relativitätstheorie Spezielle Relativitätstheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018623605&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT carmelimoshe relativitymodernlargescalespacetimestructureofthecosmos

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