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| De Felice F., Clarke C.J.S. — Relativity on curved manifolds |
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| Предметный указатель |
Klein — Gordon 410
Komar 210 328
Kronecker delta 24
Kronecker generalized delta 48
Kruskal coordinates 336
Lagrangian coordinates 195
Lagrangian formulation 189ff
Lagrangian of a perfect fluid 196 197
Lagrangian of an electromagnetic field 200 227
Lagrangian of the background geometry 192
Landau and Lifschitz 204 205
Left-handed coordinates see "Coordinate system"
Length measure of 2 55 275
Lewis 390
Lie 62ff
Lie algebra 151ff
Lie brackets 65 91 102
Lie group 151
Light rays 233
Light velocity 7 187 297 303
Light, bending of 354
Light-cone 236
Lindquist 402 416
Line element 56
Lipschitz 19 61
Locally non rotating frame 408 409
Lorentz force 298 300
Lorentz group 135 150
Lorentz internal rotation group 136
Lorentz transformations 7
Lorentz transformations, proper and orthocronous 135
Lorentzian metric 45
Lowering of a tensor see "Contraction"
Manifold 19ff
Manifold, differentiable 19
Manifold, imbedded 21
MAP 15
Map of manifolds 20
Map, bilinear 33
Map, exponential 108
Map, linear 22
Map, the dual map 31
Map, the tangent map 27
Marginally stable orbits in the Kerr metric 416
Mass in geometrized units 361
Mass in the Kerr metric 399
Mass of an extended body 217
Mass, generalized mass in the Reissner — Nordstroem metric 361
Mass, gravitational 8
Mass, inertial 8
Mass, irreducible 412
Mass, total in Schwarzschild 325
Matrix algebra 49 50
Matrix, Laplace expantion of 50
Matrix, non-singular 26
Maxwell equations 227 232 233
Maxwell equations, (Einstein) — Maxwell 358 421
Measure of length 2 55ff
Measure, theory of 274ff
Metric tensor 39
Michaelson — Morley 7
Module 57
Modulus of a vector 40
Momentum of a fluid 301
Momentum, angular 209 214 343 406 407 408 417 423
Momentum, angular in the Kerr metric 400
Momentum, linear of a particle 297
Momentum, proper 213
Motion, constants of 213 225 343 352 406 407 420
Motion, equations of motion for a fluid 304ff
Motion, equations of motion for a particle 221ff
Motion, equations of motion for extended bodies 211ff
Motion, slow motion approximation 307ff
Neighbourhood 14
Neighbourhood, coordinate 17
Neighbourhood, normal 83
Newman 421
Newtonian limit of the gravitational field 313
Nordstroem see "Reissner — Nordstroem solution"
Null, cone see "Light-cone"
Null, curve 45 (see also "Geodesics")
Null, geodesic see "Geodesics"
Null, principle directions in the Kerr metric 420 421
Null, subspace 45
Null, tetrad 263
Observer 130
Observer in plunging orbits 349
Observer, definition of 130
Open sets 14
Operator projecting parallel and transverse 130
Optical scalars 266
Orbits see "Geodesics"
Orbits, marginally stable 416
Orientability of a manifold 45
Orthogonality 40
Orthonormal basis 43 (see also "Tetrad")
Palatini identity 192
Papapetrou 215 390 421
Paracompactness 15 129
Parallel vector 85
Parallelism 85ff
Parameter on a congruence 62
Parameter on a curve 21
Parameter, transformation to an affine parameter 75 76
Particle horizon 383 385
Penrose 166 271 338 409 412
Penrose diagrams 338ff
Penrose flag 166
Penrose process of energy extraction 409
Perfect fluid see "Fluids"
Petrov classification 146 177ff
Planck 426 427
Plato 1
Poincare 2 3
Pole-dipole approximation 220
Potential curves for time-like geodesics 345 414
Potential curves in general relativity 192
Potential curves, Newtonian 255 313
Potential curves, one-form in electromagnetism 200 227ff 422 423
Potential curves, velocity potentials 198
Precession of the apsidal points 347
Principal null directions 180 405 421
Principle of equivalence 10
Principle of general covariance 11
Principle of relativity 297
Pseudotensor 201 205
Quadrupole moment of extended bodies 215 218
Quadrupole moment of gravitationally radiating sources 318
Radiation, cosmic 378
Radiation, electromagnetic 231ff
Radiation, gravitational 314ff
Raising (of a tensor) see "Contraction"
Rank (of a tensor) 36
Raychauduri equation 257 267 272
Red-shift in cosmology 385
Reissner — Nordstroem extended solution 361
Reissner — Nordstroem singularity 369
Reissner — Nordstroem solution 358
Retarded potentials 231 315
Reversible processes in black-holes 412
Ricci rotation coefficients 140 251
Ricci tensor 111
Ricci tensor, tetrad decomposition of 259 260
| Riemann integral 54
Riemann tensor 104
Riemann tensor, tetrad decomposition of 250ff
Riemannian manifold 44 85
Right-handed coordinates 45
Robertson 320 376 384
Robinson 424
Rotation group 320
Rotational effects 243
Rotational effects in the Kerr metric 408
Sachs see "Goldberg — Sachs theorem"
Sato 425
Scalar curvature 112
Scalar product 40
Schild 405
Schwarzschild extended external solution 332
Schwarzschild external solution 322ff
Schwarzschild internal solution 326
Schwarzschild radius 332 333
Segre symbols 183 184
Shear 256 257 266 278 302 305 319
Shear, free congruence 374 376 420
Shoen 272
Signature 43
Simultaneity 277
Singularity 267ff
Singularity in cosmology 380
Singularity in Kerr 400
Singularity in Reissner — Nordstroem 369
Singularity in Schwarzschild 332
Singularity, apparent 332 361 401
Singularity, crushing 270
Space of r-forms 51
Space, compact 15
Space, concept of space in theory of measurements 275ff
Space, connected 14 129
Space, maximally symmetric 125
Space, paracompact 15 129
Space, separated (Hausdorff) 14 129
Space, topological 14 129
Space-like curve 45
Space-like subspace 45
Space-time 4 129
Special relativity 4 187
Spherical symmetry 320 329
Spherically symmetric line element 322
Spin entanglement 160
Spin frame 160
Spin vector 219 221
Spin-curvature interaction 214ff
Spinors 146 159
Spinors, conformal 174
Spinors, connection 166
Spinors, curvature 168
Static space-times 239
Stationary space-times 240
Stationary, limit of stationarity 244
Stationary, null surfaces 244ff
Stokes 111
Stress-tensor see "Energy-momentum tensor"
Strong energy condition 269
Structure coefficients 65
Summation convention 23
Superpotential 204 205
Superradiance 409 410
Surface gravity 246 249 427ff
Symmetrization of tensors 38 39
Symmetry, axial 239 389
Symmetry, operations 37
Symmetry, spherical 320
Symmetry, symmetric spaces see "Spaces"
Tangent space 12 21
Tangent vectors 22
Temperature: effective for black-holes 427
Tensors 11 32ff
Tensors, alternating 48
Tensors, function of two points 77 120
Tensors, product 33
Tetrad 129ff
Tetrad, Fermi transported 138 139 145 286
Tetrad, null 263
Thermal spectrum 426
Thermodynamic laws 186 197 304 305
Thomas precession 221
Thorndyke see "Kennedy — Thorndyke"
Tidal stresses 254 350 351
Time orientability 45
Time, absolute 6
Time, measure of 275ff
Time, proper 224 277
Time, standard cosmic time 374
Time-like curve 45 (see also "Geodesics")
Time-like subspace 45
Tomimatsu 425
topology 14
Topology, induced 14
torque 214
Torsion 82 172
Transformations of alternating tensor 48
Transformations of contravariant indices 26 28
Transformations of covariant indices 31 32
Transformations of spinors 164
Transformations of tensor components 34 36
Transformations of the connector 77ff
Transformations, Galileo 6 7
Transformations, Lorentz 7 135
Transverse-traceless see "Gauge"
Trapped surface 271 272
Units, geometrized for angular momentum 400
Units, geometrized for electric charge 361
Units, geometrized for mass 361 396
Units, Planckian 426
Universe 372ff
Universe, closed 381
Universe, open 381
Valence 36
Vector, cotangent 28
Vector, null 40
Vector, space 22ff
Vector, space-like 45
Vector, tangent 21
Vector, time-like 45
Velocity, composition law 295ff
Velocity, Doppler velocity 289 386
Velocity, measure of relative velocities 287ff
Velocity, recession velocity 288 289 386
Vorticity 140 253 259
Vorticity in the weak field limit 310
Vorticity, free congruence 140 268
Walker 320 376 384
Weak energy condition 269
Weak field limit 306
Wedge product see "Exterior product"
Weyl solutions 424
Weyl spinor 177
Weyl tensor 111ff 180 181 254
Weyl tensor, classification of 180 181
Weyl tensor, electric and magnetic parts 254 255
White-holes 338
World-function 55ff
World-function in theory of measurements 275ff
World-function, covariant derivatives of 120
Yau 272
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