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Foster J., Nightingale J. Ч A Short Course in General Relativity (Longman mathematical texts)
Foster J., Nightingale J. Ч A Short Course in General Relativity (Longman mathematical texts)

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Ќазвание: A Short Course in General Relativity (Longman mathematical texts)

јвторы: Foster J., Nightingale J.

јннотаци€:

This textbook provides an excellent introduction to a topic that is extremely easy to get bogged down in. I took a one semester course that used this text as an undergraduate, during which I thought the book was merely decent, but then when I took a gradute course that used Carroll's Spacetime and Geometry is when I really came to appreciate the preparation this book gave me (not that Carroll's book is bad, I just wouldn't recommend it for a first reading). Not to mention the book is pretty cheap as far as physics texts go.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1979

 оличество страниц: 210

ƒобавлена в каталог: 06.03.2014

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$(Del)^{2}$ ($\nabla^{2}$)      86
$f: T \rightarrow \mathbb{R}$ symbol      6
$\mathbb{R}$ (the field of real numbers)      2 6
Absolute derivative      39 41
Acceleration in rotating frame      66
Addition of velocities      168Ч169
Affine connection      40
Affine parameter      49
Age of universe      157Ч158
Arc length      37 49
Background radiation      149
Basis vectors      3Ч12 21 22 34
Basis, change of      3 4 8 14 21 22
Basis, natural      34
Bending of light      xv 117Ч120
Bianchi identity      78
Black holes      93 113 123Ч127
Blueshift      102Ч105
Boosts      166Ч167 179
Cartesian coordinate system      54
Cartesian product      9
Centrifugal force      66
Charge density      181 182
Chart      29 93
Christoffel symbols, first and second kind      46Ч47
Coderivative      see "Covariant derivative"
Components of a tensor      12Ч16 37
Components of a vector      3 8
Compton effect      111
Connection coefficients      39 40 45Ч46
Conservation of energy-momentum      177
Continuity equation      73 74 152
Continuum, 4-dimensional spacetime      163
Contraction of tensors      15
Contraction, Lorentz      170Ч171
Contravariant tensors (tensors of type (r, 0))      12
Contravariant vectors      7 36
Coordinate systems      27Ч28 54 60 128 150
Coordinate, curve      34
Coordinate, neighbourhoods      29 31Ч33
Coordinate, ranges      93
Coordinate, velocity (of light)      98 114
Coordinate, velocity (of particles)      72 109Ч110 175
Coriolis force      66 67
Cosmological constant      158
Cosmological principle      150
Cosmology      148Ч162
Covariance, principle of general      xv
Covariant derivative      44 76
Covariant tensors (tensors of type (0, s))      12
Covariant vectors      7 36
Curl      69
Current 4-vector      182
Curvature      25Ч28
Curvature scalar      79
Curvature tensor, Riemann Ч Christoffel      76Ч77
Cyclic identity      77
d'Alembertian      135 182
Deceleration parameter      154 156 162
Deflection of light      xv 117Ч120
Density, charge      181 182
Density, critical      154 156
Density, mass      72 183
Derivatives, absolute      39Ч43
Derivatives, covariant      44 76
Distance in Schwarzschild field      96Ч97
Divergence      47 76
Doppler effect      178Ч180
Doppler effect, transverse      180
Dual spaces      6Ч8
Dummy suffices      4
Eddington Ч Finkelstein coordinates      124
Einstein cosmological model      157Ч158
Einstein summation convention      2
Einstein tensor      79
Electromagnetic field tensor      182 184
Electromagnetic potential      182
Elevator, freely falling      xii
Energy and mass      175 176
Energy-momentum 4-vector      72 175
Equations of motion of fluid      73Ч76 152
Equations of motion of particle in gravitational field      105Ч112
Equivalence of Euler Ч Lagrange and geodesic equations      51
Equivalence principle      xiЧxiii
Euler equation for fluid      75
Euler Ч Lagrange equations      50 69 106
Event      54 163
Expansion of universe      158
Falling particle      107Ч110
Field equations, Einstein      82Ч85 151
Flatness      25Ч28 77
Fluids      72Ч76 148
Force, Lorentz      183
Four-force      57 176
Four-vectors      71Ч72 174Ч176 182
Friedmann equation      152
Friedmann models      153Ч157
Functionals, bilinear      9
Functionals, linear      6
Functionals, trilinear      11
Functions, vector space of      6
Fundamental theorem of Riemannian geometry      46
Galilean transformation      168 183
Galileo      xii
Gauge condition, Lorentz      135 181
Gauge transformations      134 181
Gauge TT      138
Geodesic      48Ч49
Geodesic and Newton's laws      59
Geodesic coordinates      48
Geodesic deviation      26 79Ч81
Geodesic deviation (Newtonian)      84
Geodesic effect      xvi 120Ч123
Geodesic postulate      57
Geodesic, equation of      49 57 80
Gradient      36
Gravitational mass      xi
Gravitational radiation      132Ч147
Gravitational redshift      100Ч105
Gravitons      147
Gyroscope experiment      120Ч123
Homogeneity of space      148 150
Horizon, event      126Ч127
Horizon, particle      162
Hubble's constant      149 156 162
Hubble's Law      149 154 157 158
Hydrodynamical equations      75Ч76
Hypotheses of general relativity      xiii xv 57
Hypotheses of special relativity      163Ч164
Impossibility of transforming away gravity      xiii 129
Inertia tensor      21
Inertial frame of reference      54 55 163
Inertial mass      xi
Inner product      17Ч19 165
interval      37 164Ч165
Invariant quantities      164 165
Isomorphism, natural      8
Isotropic coordinates      91 128
Isotropy of space      149 150
Kepler's third law      110
Kronecker delta      4 16 19
Kruskal coordinates      129
Lagrange's equations      50 69 106
Lagrangian      50
Length in special-relativity      170Ч171
Length near star      94Ч97
Length of a curve      37
Length of a vector      19
Light cone      125 172Ч173
Light ray, path of      113Ч114 117Ч120
Line element      37 164Ч165
Linear dependence      2
Linear independence      2
Linear transformations      3Ч8 10Ч16 22 35
Lorentz force      183
Lorentz gauge condition      135 181
Lorentz transformation      166Ч168 179
Lowering suffices      18
Manifold      29Ч33
MAP      29Ч33
Mass and energy      72 175 176
Mass, control knob      92
Mass, gravitational      xi 71 91 186
Mass, inertial      xi 71 91 186
Matrix notation      5 14
Maxwell's equations      56 181Ч182
Mercury, perihelion of      xv 115Ч117
Metric in rotating frame      65Ч66
Metric, connection      45Ч48
Metric, Minkowski      54 164
Metric, Robertson Ч Walker      150
Metric, Schwarzschild      86Ч89 94
Metric, tensor      17Ч19 36 82
Metric, tensor field      36
Missing matter      157
Moment of inertia      20Ч23
Momentum      72 175 177
Newton's law of universal gravitation      63Ч64
Newton's laws of motion      59Ч60 163 176
Newtonian cosmology      158Ч160
Newtonian geodesic deviation      84
Newtonian orbit      110 115 130
Newtonian potential      63 82
Newtonian vertically falling particle      109
Notation      xvi 2 3 44 54 71
Null cone      125Ч126 172
Null coordinate      91
Null curve      37
Null geodesic      58
Null vector      19 58 173
Olber's paradox      149
Orbits of particles      110Ч112
Orbits of photons      113Ч115
Order of tensors      12
Orthogonal vectors      20
Orthonormal basis vectors      21
Parallel transport      43
Parallelism      38Ч43
Particle motion in gravitational field      105Ч112
Perihelion advance      xv 107 115Ч117
Photons, motion near star      113Ч115
Poincare transformations      166
Poisson's equation      85Ч86
Polarisation, electromagnetic waves      139Ч140
Polarisation, gravitational waves      137Ч141
Potential, electromagnetic      135 139 182
Potential, Newtonian      60Ч63 82
Preferred coordinates      xiv
Principle of equivalence      xiЧxiii
Principle of general covariance      xv 56
Products, tensor      9Ч11 133
Proper time      xiii 56Ч57 71 96 98 101 105 106 150 165 170
Quotient theorem      13 77
Radar sounding      xvi 98Ч100
Radiation from dumb-bell      144
Radiation, gravitational      132Ч147
Radius of orbit      111 120
Radius, Schwarzschild      123
Raising suffices      18
Rank of tensor      see "Order of tensor"
Redshift      102Ч105
Ricci tensor      78 83
Riemann Ч Christoffel curvature tensor      77
Riemannian manifold      37
Robertson-Walker line element      52 150
Rotating reference system      64
Scalar (as type (0, 0) tensor)      12 72
Scalar field      35
Schwarzschild radius      123
Schwarzschild solution      63 86 89 94
Second moment of mass distribution      133 143
Simultaneity      170 174
Space, 3-dimensional      94 163
Spacelike coordinate      91
Spacelike vector      58 173
Spaces, tensor      9Ч15
Spaces, vector      1Ч9
Spacetime, curved      25Ч28 54Ч59 150
Spacetime, diagram      100 102 111 114 171Ч174
Spacetime, flat      25Ч28 54Ч55 163Ч164 173
Spectral shift      xvi 100Ч105
Speed of gravitational waves      136
Speed of light (flat spacetime)      163
Speed of light (in gravitational field)      98 114
Speed, angular      122
Straightest lines      25Ч28 48Ч49
Stress-energy-momentum tensor for dust      90
Stress-energy-momentum tensor for fluid matter      73 75
Tachyons      58 186
Tangent space      33Ч37
Tangent vector      34
Tensor fields      33Ч37
Tensor product ($T \bigotimes U$)      9Ч11 133
Tensor, examples      14 20
Tensors of type (r, s)      12 77
Tensors, associated      19
Tensors, contraction of      15
Tensors, defined      11Ч12
Tensors, formed by differentiation      38
Tensors, mixed      12
Tensors, symmetric, skew symmetric      16Ч17
Tensors, transformations of      11 13 35
Test particle      60
Time in rotating frame      67
Time, coordinate      xiii 71 94Ч97 98 101
Time, cosmic      150
Time, delay of, near star      xvi 98Ч100
Time, dilation      67 170
Time, Newtonian      163
Time, proper      xiii 56Ч57 71 96 98 101 105 106 165 170
Timelike coordinate      91
Timelike geodesic      58
Timelike vector      58 173
Total energy of universe      160
Transformations of basis vectors      3 4 8 11 35
Transformations of components      13 14 35
Transformations, Galilean      168 183
Transformations, gauge      134 181
Transformations, Lorentz      166Ч168 179
Transformations, Poincare      166
TT gauge      138
Unit vector      19
Universe, properties of      149
Vectors and vector spaces      1Ч5
Velocity, coordinate      72 98 109Ч110 175
Velocity, world      72 175
Wave equation      136 181
Wave, 4-vector      137 175
World lines      111 125 165 173
World velocity      72 175
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