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Hughston L.P., Tod K.P., Bruce J.W. — An Introduction to General Relativity
Hughston L.P., Tod K.P., Bruce J.W. — An Introduction to General Relativity

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Название: An Introduction to General Relativity

Авторы: Hughston L.P., Tod K.P., Bruce J.W.

Аннотация:

This long-awaited textbook offers a concise one-semester introduction to basic general relativity suitable for mathematics and physics undergraduates. Emphasis is placed on the student's development of both a solid physical grasp of the subject and a sophisticated calculational facility. The text is supplemented by numerous geometrical diagrams and by a large selection of challenging exercises and problems.


Язык: en

Рубрика: Физика/Гравитационное взаимодействие/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 183

Добавлена в каталог: 11.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$E=mc^{2}$      2
Absolute derivative      71 78
Accelerated frames of reference      94
Adiabatic flow      42 44
Affine parametrization      73 f. 112 162
Age of one’s head, as compared with feet      111
angular momentum      44 135 142
Anisotropic cosmologies      170 f.
Arc length      15
Area distance      160—161
Area theorem      149
Bending of light      1 117
Bernoulli’s theorem      18
Bianchi classification of 3-dimensional Lie algebras      171 f.
Bianchi identity      59 88 90
Bianchi type I cosmologies, general solution for ideal fluids      179
Black hole explosions      149
Black holes      100 129 133—136 142
Blue shift (relativistic)      27
Boltzmann’s constant      41 91
Boyer — Lindquist coordinates for the Kerr solution      142—143
Cartan calculus      87 f.
Cartesian tensors      10 f.
Central pressure of star      141
Centre of mass, relativistic      44
Chandrasekhar, S.      135
Charge conservation      17
Charge, units for      18
Christoffel symbols      53 f. 90 101
Circular null geodesies      124
Classical tests of general relativity      117 f.
Closed time-like curves      145
Co-moving coordinates      155
Commutators of Lie derivatives      68
Commutators of skew products for symmetric tensors      70
Commutators of vector fields      10 68 79 107 108 170
Complex transformations      43
Compton scattering      30
Conformal invariance of null geodesies      74 131
Conformal Killing vectors      69
Conformal tensor (Weyl tensor)      95 100 141 169 181
Conformal transformations      65 75 131 136 169
Congruences of time-like geodesies      99 169
Connection      53 f. 93
Connection one-forms      87 f.
Constants of the motion      74 75 83 108 114—116 117 123 131
Continuity equation      40
Contravariant vectors      48
Coordinate patches      6 f. 46 57 126
Coordinate transition functions      46 f. 144
Cosmic censorship      135
Cosmological constant      168—169
Cosmological red shift      158 f.
Coulomb (unit of charge)      18
Covariant differentiation      6 53
Covariant vectors      49
Covariantly constant vectors      66
Critical density of universe      167
Current vector of a relativistic fluid      69 74
Curvature singularity      177
Curvature tensor      63 f.
de Donder gauge      103
De Motu, Newton’s remarks on the n-body problem      4
Death, by radial injection into a black hole      135
Deceleration parameter      167 f.
Deflection of light      1 117 121—122
Determinants      12—13 22
Differentiable manifold      6 46 48
Differential forms      86 f. 144
Differential geometry      2
Div, grad, curl, and all that      14
Divergence of a vector field      66 91
Dominant energy condition      100
Doppler effect      26 109 111
Duality      39 150
Dust      163 f. 176
d’Alembertian operator      103
Eddington — Finkelstein coordinates      127 f. 144
Eddington, A.      1
Einstein manifold      69
Einstein summation convention      10
Einstein tensor      9 64
Einstein — Cartan theory      56 94
Einstein, A.      2 f. 10 24 46 94 142 149 168
Einstein’s field equations      9 94 96
Electromagnetic field tensor      35 f.
Electromagnetic four-current      36 f.
Electrostatic unit (esu)      18
Ellipses, axes of      4 120 125
Energy conservation      26 f. 158
Energy density, electromagnetic      17
Energy density, fluid      9 40 74 91 157 163
Energy extraction from a black hole      147—149
Enthalpy, relativistic      42 44 68 75
Entropy, relativistic      41 f. 44 75 91
Epsilon identities      10 12 22 38—39 65—66
Equations of state      41 45 163
Equivalence principle      94 111
Ergosphere, of black hole      147—148
Eulers’s equation for ideal fluid, non-relativistic      9 18
Eulers’s equation for ideal fluid, relativistic      9 40 69
Event horizon      134—136 147 160
Exact solutions, Einstein’s remark on their difficulty      142
Extended Schwarzschild solution      126 f.
Exterior differentiation      52 88
Fine structure constant      17
First integrals      74 75 144—116
Focussing of geodesies      100 169
Foliations      19
Forms      85 f.
Four-momentum      26 f.
Friedmann equation      163
Friedmann — Robertson — Walker metric (FRW metric)      157 f. 163 174
Fundamental observers      155 169
Fundamental theorem of Riemannian geometry      8 67 94
Gauge transformations      16 103
Gauss theorem      16
Gauss, C.F.      2
Gaussian curvature      84
Generator of null cone      25
Geodesic deviation      76 f. 97 99 103
Geodesic equation      43 44 73—75 94—95 101 157 162
Geodesic field orthogonal to three Killing vectors      75
Geodesic hypothesis      73 93
Geometrical optics      162
Grassmann algebra      86
Gravitational collapse      133 f.
Gravitational constant      9 21 93—94 102 106—107 169
Gravitational waves      9 103
Habicht, C.      3
Hausdorff spaces      46
Hawking radiation      149
Helmholtz’s theorem, non-relativistic      20 23
Helmholtz’s theorem, relativistic      68—69
Herbert Spencer lecture, by Einstein      2
Hermitian matrices      22
Hilbert space      149
Homogeneity      151 f.
Homothetic Killing tensor      75
Hubble parameter      167 f.
Hubble, E.      2 168
Hubble’s law      171
Hydrostatic equilibrium      139 f. 142
Hypersurface orthogonality      90 107 175 179
Index free notation      85 f.
Index raising and lowering      25
Inertial trajectories      31
Initial value problem for Maxwell’s equations      23
Integral theorems of vector calculus      15
Interior solutions      137 f. 142
Invariant one-forms      173
Inverse of matrix      13
Isentropic flow      44 68
Isotropic three-spaces      151 f. 155
Jacobi identity      70 170
Jacobian matrix for coordinate transition functions      49 f.
Kasner metric      175 f.
Kepler’s laws      4 124
Kerr solution      135 142
Kerr — Eddington coordinates      144
Kerr — Schild coordinates      145 f.
Kerr — Schild metrics      149—150
Killing tensors      43 69 83 150
Killing vectors      43 65 66 68 74 107—108 114 139 144—145 150 170
Kronecker delta      10 25
Lagrangians for geodesic equation      74 112 117
Lagrangians for Lorentz equation      116
Lagrangians for Newtonian orbits      123
Laplace’s equation      19
Le Verrier, U.J.J.      5 117
Leibniz property for covariant derivatives      55
Leibniz property for Lie derivatives      67
Leibniz property for skewed second covariant derivatives      61
Levi-Civita connection      8 60 63 69—70
Lie derivative      52 67 84 107
Lie groups      170 f.
Lie propagation      84
Light, time taken to travel around the universe      168
Light-cone      25 160 162
Linearized theory      103
Longitudinal and transverse components      31
Lorentz contraction      32 f.
Lorentz equation for charged particles, non-relativistic      17 23
Lorentz equation for charged particles, relativistic      40 45 99 116
Lorentz factor      26
Lorentz gauge condition      162
Lorentz transformations      32
Lorentzian metric      7 26 67
Luminosity distance      162
Magic density      167
Manifolds      46 f.
Mathematics, Einstein’s repect for      46
Matrices      12 f.
Maximally symmetric spaces      153
Maxwell, J.C.      35
Maxwell’s equations      16 f. 22 64 104
Metric connections      8 63 149
Metric tensor      7—8 25
Minkowski, H.      1 f. 24
Momentum, relativistic      26 f.
Multi-fluid cosmologies      169 179
Music, relation to creative process      3
n-sphere      48 91 153
n-torus      48
Navier Stokes equation      23
Newcomb, S.      117
Newton — Poisson equation      8 21 93 101 137
Newton, I.      4 5
Newtonian gravitation      4—5 20—21 92 98—99 101 116 117 124—125
Nonlinear character of Einstein’s theory      149
Normal vector to a surface      15
Null cones      1 25 160 162
Null geodesies      25 109 112 124 126 132 158 162
Null surfaces      131 147 150 159
Number density      41 91
Oblate ellipsoids      143
Oblate stars      116 124
Occam’s rasor, and torsion      94
Olympian Academy      3
Oppenheimer — Volkoff equation      139 f.
Orgies of formalism, Weyl’s remark      85
orthogonal matrices      22 170
Oxford University and a professor’s time machine      43
Oxford University and Einstein      2
p-forms      85 f.
Parallel propagation      81
Parallelepiped, volume of      12
Particle horizon      160
Particle interactions      27 f.
Pascal, B., on the universe as a hypersphere      151
Penrose, R.      147—149 181
Perihelion advance      3—6 117
Permutation tensor      10 12 22 38—39 65
Pfaffs theorem      50
Photon, emission and reception      27 109—111
Plancks’s constant      17 31 111
Plato      3 5
Potential vorticity      75
Poynting vector (electromagnetic energy flux)      17 100
Pressure      9 41 18 100 137 163
Principal null directions of electromagnetic field      44—45
Principal null directions of gravitational field      146—147
Probabilistic interpretation of quantum mechanics      149
Projection operator      31
Projective space ($RP^{n}$)      48
Projectively flat manifold      61
Proper length      32
Proper time      31
Quantum gravity, Einstein’s thoughts      148—149
Rank of a tensor      50
Red shift      8 109 133 158
Rest mass      26 f.
Ricci identities      58 f.
Ricci rotation coefficients      87 f.
Ricci scalar      64 100
Ricci tensor      60 64 99
Riemann tensor      57 f. 84 89 99
Riemann, B.      2
Riemannian connection      8 60 63
Ring singularity of Kerr solution      143
Rotating star      108 111 142
Rotation of geodesies      100 169
Scalar fields      48
Scalar triple product      11
Schwarzschild radius      106 f.
Schwarzschild solution      104 f.
Schwarzschild solution, interior      137 f.
Self-gravitating fluids      20 137
Seneca, on instability      133
Shearing of geodesies      100 169
Singularities      133 f. 143 177
Slow motion approximation      101 f.
Smoothness      48
SO(N)      154 170
Solo vine, M.      3
Sommerfeld, A.      46
Space-time continuum      6 24
Spaces of constant curvature      151
Special relativity      24 f.
Specific volume      41 91
Spherical symmetry      88 f. 104 116 133—135 138 151
Steady flows      19
Stellar inequalities      140—141
Stokes theorem      16
Stress tensor for electromagnetism      23 39 43.
Stress tensor for ideal fluid      9 20 40 68 157
Stress tensor for self-gravitating fluid      20 f.
Stress tensor for viscous fluid      23
Summation convention      10
Sun, bending of light      122
Sun, gravitational red-shift      111
Sun, Schwarzschild radius      106—107
Symplectic structure, associated torsion      66
Tangent vectors, to curves      71
Temperature, of relativistic fluid      41 f. 91
Tensor calculus      6 f. 10 24 46 85
Thermal radiation      169
Thermodynamical fluid      41 45 92
Time delay      124
Time dilation      8 33 110 158
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