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Relativity on Curved Manifolds : Cambridge Monographs on Mathematical Physics - F.De Felice

Relativity on Curved Manifolds

Cambridge Monographs on Mathematical Physics

Paperback Published: 31st August 1992
ISBN: 9780521429085
Number Of Pages: 459

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General relativity is now essential to the understanding of modern physics, but the power of the theory cannot be exploited fully without a detailed knowledge of its mathematical structure. This book aims to implement this structure, and then to develop those applications that have been central to the growth of the theory.

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' ... a useful book with some unusual features which will win it a place on relativists' shelves and may be of interest to mathematical physicists in general.' Contemporary Physics

Prefacep. xi
Geometry and Physics: An Overviewp. 1
Geometryp. 1
Special relativityp. 4
General relativityp. 7
Local, global and infinitesimalp. 11
The Background Manifold Structurep. 14
Topological spacesp. 14
Mapsp. 15
Coordinate neighbourhoodsp. 17
Differentiable manifoldsp. 19
Maps of manifoldsp. 20
The tangent spacep. 21
Bases in the tangent spacep. 24
Transformation properties of vector componentsp. 25
The tangent mapp. 27
The cotangent spacep. 28
Bases in the cotangent spacep. 29
The dual tangent mapp. 31
Tensorsp. 32
Symmetry operations on tensorsp. 37
The metric tensorp. 39
Raising and lowering of tensor indicesp. 47
Alternating tensorsp. 48
Exterior algebrap. 51
Measure of lengths and the world-functionp. 55
Differentiationp. 57
Tensor fields and congruencesp. 57
The Lie derivativep. 62
The connectorp. 68
Parallel propagation and geodesicsp. 72
Transformation properties of the connectorp. 77
The covariant derivativep. 78
Torsion and normal coordinatesp. 82
Compatibility of the metric with the connectionp. 84
Parallelismp. 85
Applications of the covariant derivativep. 86
The exterior derivativep. 88
Frobenius theoremsp. 90
Isometries on Mp. 99
The Curvaturep. 102
The Riemann tensorp. 102
Symmetry properties of the Riemann tensor and the Gaussian curvaturep. 106
Significance of a curvature tensor vanishing everywherep. 109
The Ricci tensor, the curvature scalar, the Weyl tensorp. 111
The Bianchi identitiesp. 114
The equation of geodesic deviationp. 117
The covariant derivative of the world-functionp. 120
Maximally symmetric spacesp. 125
Space-time and Tetrad Formalismp. 129
The space-time manifold and the physical observerp. 129
Construction of a tetradp. 133
Relations among tetrads and the Lorentz groupp. 135
The propagation laws for tetradsp. 138
The Ricci rotation coefficientsp. 139
Differential operators related to a tetrad framep. 141
Spinors and the Classification of the Weyl Tensorp. 146
Outlinep. 146
The group SL (2, C)p. 146
Lie algebrasp. 151
Bivector algebrap. 155
Spinorsp. 159
The spinor connectionp. 166
The spinor curvaturep. 168
The torsion casep. 172
Conformal spinorsp. 174
The Weyl spinor and the Petrov classificationp. 177
Coupling Between Fields and Geometryp. 185
Newtonian fluidsp. 185
Generalization to special relativityp. 187
Coupling between fields and geometry: the field actionp. 188
The gravitational action and the Einstein equationsp. 191
The energy-momentum tensor of a perfect fluidp. 195
The energy-momentum tensor of a single particlep. 198
The energy-momentum tensor of the electromagnetic fieldp. 200
The energy-momentum pseudotensorp. 201
Dynamics on Curved Manifoldsp. 206
Conservation lawsp. 206
The equations of motion of an extended bodyp. 211
The centre-of-mass descriptionp. 216
Motion of a point particlep. 221
Constants of motionp. 225
Maxwell's equations for a free electromagnetic fieldp. 227
Maxwell's equations in the presence of charges and currentsp. 228
The radiation fieldp. 231
The light conep. 236
Stationary space-timesp. 238
The geometry of stationary null surfacesp. 244
Geometry of Congruencesp. 250
Tetrad decomposition of the Riemann tensorp. 250
The expansion equationp. 255
The vorticity equationp. 258
The Einstein equations in tetrad formp. 259
The geometry of null raysp. 261
Singularitiesp. 267
Physical Measurements in Space-timep. 274
The concept of measurementp. 274
The measurement of time intervals and space distancesp. 275
Measurements of anglesp. 281
Curvature effects in the measurement of anglesp. 282
Measurement of frequencyp. 286
Measurement of relative velocitiesp. 287
The velocity composition lawp. 295
Energy and momentum of a particlep. 297
Measurement of electric and magnetic fieldsp. 298
The properties of a fluidp. 300
The equations of motion of a fluidp. 304
The small curvature limitp. 306
Gravitational radiationp. 314
Spherically Symmetric Solutionsp. 320
The spherically symmetric line elementp. 320
The external Schwarzschild solutionp. 322
The internal Schwarzschild solutionp. 326
The global structure of spherically symmetric space-timesp. 329
The extended external Schwarzschild solutionp. 332
Penrose diagramsp. 338
Time-like geodesics in the external Schwarzschild solutionp. 342
The precession of the apsidal pointsp. 347
The plunging-in observerp. 349
Null geodesics in the external Schwarzschild solutionp. 351
The bending of light raysp. 354
The Reissner-Nordstrom solutionp. 358
The extended Reissner-Nordstrom solutionp. 361
Particle behaviour near the Reissner-Nordstrom singularityp. 369
Homogeneous and isotropic cosmologyp. 372
The Friedmann solutionsp. 378
Cosmological effectsp. 384
Axially Symmetric Solutionsp. 389
The axially symmetric line element: the canonical formp. 389
The Kerr solutionp. 392
Physical interpretation of the Kerr metricp. 397
The space-time structurep. 400
Time-like geodesicsp. 406
Rotationally induced effectsp. 408
The angular geodesic equationp. 413
The equatorial circular geodesicsp. 414
Null geodesicsp. 418
The Kerr-Newman solutionp. 421
The Weyl and the T-S solutionsp. 424
Hawking radiation: an overviewp. 426
Notationp. 431
Referencesp. 434
Indexp. 441
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521429085
ISBN-10: 0521429080
Series: Cambridge Monographs on Mathematical Physics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 459
Published: 31st August 1992
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 23.06 x 15.49  x 2.87
Weight (kg): 0.68

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