A First Course in General Relativity

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  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2009-06-22
  • Publisher: Cambridge University Press
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Clarity, readability and rigor combine in the second edition of this widely-used textbook to provide the first step into general relativity for undergraduate students with a minimal background in mathematics. Topics within relativity that fascinate astrophysical researchers and students alike are covered with Schutz's characteristic ease and authority - from black holes to gravitational lenses, from pulsars to the study of the Universe as a whole. This edition now contains discoveries by astronomers that require general relativity for their explanation; a revised chapter on relativistic stars, including new information on pulsars; an entirely rewritten chapter on cosmology; and an extended, comprehensive treatment of modern detectors and expected sources. Over 300 exercises, many new to this edition, give students the confidence to work with general relativity and the necessary mathematics, whilst the informal writing style makes the subject matter easily accessible. Password protected solutions for instructors are available at www.cambridge.org/9780521887052.

Table of Contents

Preface to the second editionp. xi
Preface to the first editionp. xiii
Special relativityp. 1
Fundamental principles of special relativity (SR) theoryp. 1
Definition of an inertial observer in SRp. 3
New unitsp. 4
Spacetime diagramsp. 5
Construction of the coordinates used by another observerp. 6
Invariance of the intervalp. 9
Invariant hyperbolaep. 14
Particularly important resultsp. 17
The Lorentz transformationp. 21
The velocity-composition lawp. 22
Paradoxes and physical intuitionp. 23
Further readingp. 24
Appendix: The twin 'paradox' dissectedp. 25
Exercisesp. 28
Vector analysis in special relativityp. 33
Definition of a vectorp. 33
Vector algebrap. 36
The four-velocityp. 41
The four-momentump. 42
Scalar productp. 44
Applicationsp. 46
Photonsp. 49
Further readingp. 50
Exercisesp. 50
Tensor analysis in special relativityp. 56
The metric tensorp. 56
Definition of tensorsp. 56
The (01) tensors: one-formsp. 58
The (02) tensorsp. 66
Metric as a mapping of vectors into one-formsp. 68
Finally: (MN) tensorsp. 72
Index 'raising' and 'lowering'p. 74
Differentiation of tensorsp. 76
Further readingp. 77
Exercisesp. 77
Perfect fluids in special relativityp. 84
Fluidsp. 84
Dust: the number-flux vector Np. 85
One-forms and surfacesp. 88
Dust again: the stress-energy tensorp. 91
General fluidsp. 93
Perfect fluidsp. 100
Importance for general relativityp. 104
Gauss' lawp. 105
Further readingp. 106
Exercisesp. 107
Preface to curvaturep. 111
On the relation of gravitation to curvaturep. 111
Tensor algebra in polar coordinatesp. 118
Tensor calculus in polar coordinatesp. 125
Christoffel symbols and the metricp. 131
Noncoordinate basesp. 135
Looking aheadp. 138
Further readingp. 139
Exercisesp. 139
Curved manifoldsp. 142
Differentiable manifolds and tensorsp. 142
Riemannian manifoldsp. 144
Covariant differentiationp. 150
Parallel-transport, geodesics, and curvaturep. 153
The curvature tensorp. 157
Bianchi identities: Ricci and Einstein tensorsp. 163
Curvature in perspectivep. 165
Further readingp. 166
Exercisesp. 166
Physics in a curved spacetimep. 171
The transition from differential geometry to gravityp. 171
Physics in slightly curved spacetimesp. 175
Curved intuitionp. 177
Conserved quantitiesp. 178
Further readingp. 181
Exercisesp. 181
The Einstein field equationsp. 184
Purpose and justification of the field equationsp. 184
Einstein's equationsp. 187
Einstein's equations for weak gravitational fieldsp. 189
Newtonian gravitational fieldsp. 194
Further readingp. 197
Exercisesp. 198
Gravitational radiationp. 203
The propagation of gravitational wavesp. 203
The detection of gravitational wavesp. 213
The generation of gravitational wavesp. 227
The energy carried away by gravitational wavesp. 234
Astrophysical sources of gravitational wavesp. 242
Further readingp. 247
Exercisesp. 248
Spherical solutions for starsp. 256
Coordinates for spherically symmetric spacetimesp. 256
Static spherically symmetric spacetimesp. 258
Static perfect fluid Einstein equationsp. 260
The exterior geometryp. 262
The interior structure of the starp. 263
Exact interior solutionsp. 266
Realistic stars and gravitational collapsep. 269
Further readingp. 276
Exercisesp. 277
Schwarzschild geometry and black holesp. 281
Trajectories in the Schwarzschild spacetimep. 281
Nature of the surface r = 2Mp. 298
General black holesp. 304
Real black holes in astronomyp. 318
Quantum mechanical emission of radiation by black holes: the Hawking processp. 323
Further readingp. 327
Exercisesp. 328
Cosmologyp. 335
What is cosmology?p. 335
Cosmological kinematics: observing the expanding universep. 337
Cosmological dynamics: understanding the expanding universep. 353
Physical cosmology: the evolution of the universe we observep. 361
Further readingp. 369
Exercisesp. 370
Summary of linear algebrap. 374
Referencesp. 378
Indexp. 386
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