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Introduction to Tensor Calculus, Relativity and Cosmology : Dover Books on Physics - D. F. LAWDEN

Introduction to Tensor Calculus, Relativity and Cosmology

Dover Books on Physics


Published: 27th January 2003
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RRP $27.45

Elementary introduction pays special attention to aspects of tensor calculus and relativity that students find most difficult. Contents include tensors in curved spaces and application to general relativity theory; black holes; gravitational waves; application of general relativity principles to cosmology. Numerous exercises. Solution guide available upon request. 1982 edition.

Prefacep. ix
List of Constantsp. xiii
Special Principle of Relativity. Lorentz Transformationsp. 1
Newton's laws of motionp. 1
Covariance of the laws of motionp. 3
Special principle of relativityp. 4
Lorentz transformations. Minkowski space--timep. 6
The special Lorentz transformationp. 9
Fitzgerald contraction. Time dilationp. 12
Spacelike and timelike intervals. Light conep. 14
Exercises 1p. 17
Orthogonal Transformations. Cartesian Tensorsp. 21
Orthogonal transformationsp. 21
Repeated-index summation conventionp. 23
Rectangular Cartesian tensorsp. 24
Invariants. Gradients. Derivatives of tensorsp. 27
Contraction. Scalar product. Divergencep. 28
Pseudotensorsp. 29
Vector products. Curlp. 30
Exercises 2p. 31
Special Relativity Mechanicsp. 39
The velocity vectorp. 39
Mass and momentump. 41
The force vector. Energyp. 44
Lorentz transformation equations for forcep. 46
Fundamental particles. Photon and neutrinop. 47
Lagrange's and Hamilton's equationsp. 48
Energy--momentum tensorp. 50
Energy--momentum tensor for a fluidp. 53
Angular momentump. 57
Exercises 3p. 59
Special Relativity Electrodynamicsp. 73
4-Current densityp. 73
4-Vector potentialp. 74
The field tensorp. 75
Lorentz transformations of electric and magnetic vectorsp. 77
The Lorentz forcep. 79
The energy--momentum tensor for an electromagnetic fieldp. 79
Exercises 4p. 82
General Tensor Calculus. Riemannian Spacep. 86
Generalized N-dimensional spacesp. 86
Contravariant and covariant tensorsp. 89
The quotient theorem. Conjugate tensorsp. 94
Covariant derivatives. Parallel displacement. Affine connectionp. 95
Transformation of an affinityp. 98
Covariant derivatives of tensorsp. 100
The Riemann--Christoffel curvature tensorp. 102
Metrical connection. Raising and lowering indicesp. 105
Scalar products. Magnitudes of vectorsp. 107
Geodesic frame. Christoffel symbolsp. 108
Bianchi identityp. 111
The covariant curvature tensorp. 111
Divergence. The Laplacian. Einstein's tensorp. 112
Geodesicsp. 114
Exercises 5p. 117
General Theory of Relativityp. 127
Principle of equivalencep. 127
Metric in a gravitational fieldp. 130
Motion of a free particle in a gravitational fieldp. 133
Einstein's law of gravitationp. 135
Acceleration of a particle in a weak gravitational fieldp. 137
Newton's law of gravitationp. 139
Freely falling dust cloudp. 140
Metrics with spherical symmetryp. 142
Schwarzschild's solutionp. 145
Planetary orbitsp. 147
Gravitational deflection of a light rayp. 150
Gravitational displacement of spectral linesp. 152
Maxwell's equations in a gravitational fieldp. 154
Black holesp. 155
Gravitational wavesp. 159
Exercises 6p. 163
Cosmologyp. 174
Cosmological principle. Cosmical timep. 174
Spaces of constant curvaturep. 176
The Robertson--Walker metricp. 180
Hubble's constant and the deceleration parameterp. 181
Red shift of galaxiesp. 182
Luminosity distancep. 183
Cosmic dynamicsp. 185
Model universes of Einstein and de Sitterp. 188
Friedmann universesp. 189
Radiation modelp. 193
Particle and event horizonsp. 195
Exercises 7p. 197
Referencesp. 199
Bibliographyp. 200
Indexp. 201
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780486425405
ISBN-10: 0486425401
Series: Dover Books on Physics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 224
Published: 27th January 2003
Publisher: Dover Publications Inc.
Country of Publication: US
Dimensions (cm): 23.0 x 23.4  x 1.3
Weight (kg): 0.27
Edition Number: 3
Edition Type: Revised