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Ludvigsen M. — General relativity. A geometric approach
Ludvigsen M. — General relativity. A geometric approach

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Название: General relativity. A geometric approach

Автор: Ludvigsen M.

Аннотация:

Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear, concise and up-to-date introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. This allows the theory to be pared down and presented in its simplest and most elegant form. Topics covered include flat spacetime (special relativity), Maxwell fields, the energy-momentum tensor, spacetime curvature and gravity, Schwarzschild and Kerr spacetimes, black holes and singularities, and cosmology. In developing the theory, all physical assumptions are clearly spelled out and the necessary mathematics is developed along with the physics. Exercises are provided at the end of each chapter and key ideas in the text are illustrated with worked examples. Solutions and hints to selected problems are also provided at the end of the book. This textbook will enable the student to develop a sound understanding of the theory of general relativity, and all the necessary mathematical machinery.


Язык: en

Рубрика: Физика/Гравитационное взаимодействие/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 217

Добавлена в каталог: 18.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute time      3
Abstract index notation      56
Abstract indices      57
Affine space      28 62
Affine tangent vector      96
angular momentum      74 125 131
Angular momentum parameter      128
Angular momentum, intrinsic      77 132
Area function      136
Area theorem      159 170
Arrow of time      177
Asymptotic flatness      115
Asymptotic flatness, definition of      118
Background radiation      187 191
Beforeness      9
Bianchi identities      90
big bang      8 179
Big bang, singularity      185
Birkhoff’s theorem      134 139
Black hole      155
Black hole, entropy      170
Black hole, temperature      170
Black-hole region      158
Blackbody radiation      188
Blackbody signature      187
Blackbody spectrum      8 190 191
Boltzmann constant      188
Bondi coordinate system      121
Bondi factor      24
Bondi scaling      120
Cauchy hypersurface      150
Caustic point      158
Charge density      38
Chart      82
clock      10
Closed Universe      180
Comoving observer      7 177
Compatible symmetries      122
Compton scattering      43
Conformal completion      118
Conformal freedom      120
Conformal rescaling      110
Congruence      63 83
Congruence, parametrized      63
Connection      86
Conservation equation      70
Conserved current      77
Constant curvature      94 183
Continuity equation      70
Coordinate system      82
Cosmic censorship hypothesis      160
Cosmological constant      100 187
Cosmological principle      6 175
Cosmology      6
Covariant derivative      84 86
Covector      52
Critical density      180
Current density      37
Curvature tensor      5 89 96 137
Derivation      63 83
Directional derivative      61
Divergence      65
Divergence function      106 157
Doppler shift      25
Dust particles      103
Early Universe      7
Einstein equation      5
Einstein tensor      91
Einstein’s field equation      100
Elastic time      178
Electric charge      71
electromagnetic field      49
Energy of a gravitational field      131
Energy-momentum tensor      5 43 73 100
Entropy of photon gas      189
Entropy, per baryon      194
Entropy, specific      194
Equation of state      185 186
Equatorial Killing field      141
Ergosphere      167
Euclidean geometry      4
Euler equation      70
Event      3 12
Event, pointlike      12
Expansion factor      177
Four-acceleration      48
Four-momentum      41
Four-momentum density      43
Four-momentum of a photon      33
Four-velocity      28
Friedmann equation      183
Future null infinity      116 117
Gauss’s theorem      74 76 77 131
Generalized entropy      170
Generalized second law      171
Geodesic      96
Geodesic deviation      99
Geodesic equation      96 141
Global Cauchy hypersurface      157
Gradient      61 84
Gradient operator      86
Gravitational collapse      152
Gravitational constant      10
Gravitational entropy      177
Gravitational mass      138 140
Gravitational radiation      116
Gravitational red shift      125 143
handedness      9
Hawking effect      170
Homogeneity of the Universe      177
Hubble’s law      178
Identity tensor      53
Incomplete geodesic      156
Inertial observer      4
Inertial particle      13 96
Initial conditions      6
Intrinsic angular momentum for Kerr spacetime      163
Isotropic      6
Isotropy of the Universe      177
Kerr angular velocity      165
Kerr congruence      111
Kerr event horizon      164
Kerr mass      130
Kerr metric      130
Kerr spacetime      126 128 132 161
Killing equation      122
Killing field      77
Killing tensor      164
Killing vector      122
Killing vector, asymptotic normalization      126
Komar energy      132
Kronecker delta      36
Kruskal diagram      148
Kruskal spacetime      147
Laplace      152
Latitudinal angle      127 128 161
Leibniz condition      63 86
Levi-Cevita tensor      36 55 73 89
Lie bracket      64 88
Lie derivative      64 122
Lie propagation      66
Light-second      10
Longitudinal function      130
Lorenz transformation      36
Magnetic charge      71
Magnetic current      72
Magnetic part      59
Manifold      83
Mass parameter      128
Maxwell equations, vacuum      62
Maxwell field, Coulomb      62
Maxwell field, electric part      59
Maxwell tensor      49 54
Maxwell tensor, dual of      72
Maxwell’s equations      70 72
Metric connection      88
Metric, rescaled      118
Metric, signature      86
Naked singularities      160
Neutrino background      187
Neutron star      152
Newtonian gravity      101
Newton’s laws      100
No-hair theorem      160
Null cones      16
Null congruence, shear-free      110
Null congruence, surface-forming      106
Null fluid      101
Null function      97
Null generators      97
Null geodesies      85 97
Null tetrad      108 109
Open set      82
Open Universe      180
Orientation, spacelike      86
Orientation, temporal      86
Paracompactness      83
Parallel propagation      88
Parameter function      63
Particle horizon      181
Perfect cosmological principle      176
Perfect fluid      47 70 183
Perihelion      142
Perihelion, advance      145
photons      4
Planck’s constant      10
Planck’s law      33
Plane-wave      62
Point in space      3
Position vector      28
Position vector field      61
Pressure      48 70
Principal null directions      147
Principal null vectors      161
Principle of equivalence      81
Principle of relativity      4 14
Proper time      17
Quantum gravity      177
quantum mechanics      6
Radial function      116
Radiation-filled universe      186
Raychaudhuri equation      104 136
Raychaudhuri equation for a null congruence      108
Red shift, cosmological      178
Red-shift factor      125
Relativistic continuity equation      101
Relativistic Euler equation      101
Rest mass      41
Ricci curvature      119 120
Ricci tensor      91
Riemann zeta function      189
Scalar curvature      91
Scaling factor      177 183
Schwarzschild geometry      134 146
Schwarzschild horizon      147
Schwarzschild metric      140
Schwarzschild radius      152
Schwarzschild singularity      147
Schwarzschild spacetime      139 147
Schwarzschild throat      149
Shear of a null congruence      108
Shear of timelike congruence      104
Singular spacetime      156
Singularity theorems      8 155
Smooth space      82
Smooth structure      82
Smoothness      82
Spacetime      3
Spacetime geometry      4
Spacetime metric      4 30
Spacetime, algebraically special      111
Spacetime, axisymmetric      123
Spacetime, inextendible      85 156
Spacetime, metric      85
Spacetime, predictable      150
Spacetime, singularity      152 156
Spacetime, static      123
Spacetime, stationary      123
Spacetime, symmetry      115 122
Spherical symmetry      135
Spin      77
Standard model      6
Static universe      184
Stationary observer      125 126
Stefan — Boltzmann constant      188
Stefan — Boltzmann law      188
Streamlines      63
Strong energy condition      44 104
Summation convention      29
Surface gravity      166
Surface integral      77
Symmetry family      52
Tangent vector      84
Tensor      51
Tensor product      52
Tensor, anti-self-dual      73
Tensor, components      52
Tensor, contractions      53
Tensor, field      61
Tensor, self-dual      73
Tensor, simple      53
Tensor, trace      54
Thermal equilibrium      7
Thermodynamics of black holes      169
Thermodynamics, classical      170
Three-momentum      42
Tidal effects      81 96
Torsion-freeness      87 90
TP-symmetry      123
Trapped surface      149 157 158
Twist      111
universal time      177
Weak energy condition      43 47
Weyl tensor      92
White dwarf      152
World line      3 12
World tube      74 134
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