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| Ïîèñê ïî óêàçàòåëÿì |
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| Misner C.W., Thorne K.S., Wheeler J.A. — Gravitation |
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| Ïðåäìåòíûé óêàçàòåëü |
Curvature, formalism of Einstein tensor in terms of intrinsic and extrinsic curvature 515
Curvature, formalism of Einstein tensor interpreted as moment of rotation 373—377
Curvature, formalism of Einstein tensor introduced 222 325f
Curvature, formalism of Einstein tensor track-1 equations summarized 224
Curvature, formalism of Einstein tensor uniqueness of 405 407f
Curvature, formalism of extrinsic curvature of a hypersurface 511—516
Curvature, formalism of extrinsic curvature of a hypersurface contrasted with intrinsic curvature 336 421
Curvature, formalism of extrinsic curvature of a hypersurface from Lie derivative of metric 520
Curvature, formalism of extrinsic curvature of a hypersurface Gauss — Codazzi relations 514ff
Curvature, formalism of extrinsic curvature of a hypersurface operator for 511
Curvature, formalism of extrinsic curvature of a hypersurface tensor for 512
Curvature, formalism of fundamental equations, summarized 223—224
Curvature, formalism of Gaussian curvature of a 2-surface 30 44 336f
Curvature, formalism of intrinsic curvature of a hypersurface 509f
Curvature, formalism of invariants of Riemann 491
Curvature, formalism of Jacobi curvature operator 286
Curvature, formalism of Jacobi curvature operator in context of Newton — Cartan theory 299 301
Curvature, formalism of Jacobi curvature tensor 286f
Curvature, formalism of principal radii of curvature for a 2-surface 44 335f
Curvature, formalism of Ricci tensor 222 325f
Curvature, formalism of Ricci tensor in Newton — Cartan theory 290 300
Curvature, formalism of Riemann tensor as machine with slots 271 274f
Curvature, formalism of Riemann tensor Bianchi identities 221f 224 325f
Curvature, formalism of Riemann tensor by parallel transport around closed curve 277—282
Curvature, formalism of Riemann tensor component formula for in non-coordinate basis 277
Curvature, formalism of Riemann tensor component formulas for, summarized 224 266
Curvature, formalism of Riemann tensor defined by geodesic deviation 29—37 218f 270—277 287
Curvature, formalism of Riemann tensor dynamic components of 517f
Curvature, formalism of Riemann tensor elementary introduction to 31 34—37 39
Curvature, formalism of Riemann tensor in 2 and 3 dimensions: deducible from Ricci tensor 334 343 550
Curvature, formalism of Riemann tensor in extenso track-1 treatment (metric present) 218—224
Curvature, formalism of Riemann tensor in extenso, in absence of metric 270—288
Curvature, formalism of Riemann tensor in extenso, properties induced by introduction of metric 324—327
Curvature, formalism of Riemann tensor in linearized theory 438
Curvature, formalism of Riemann tensor in Newton — Cartan spacetime 290 302
Curvature, formalism of Riemann tensor invariants of 491
Curvature, formalism of Riemann tensor number of independent components 326
Curvature, formalism of Riemann tensor only tensor from, and linear in, second derivatives of metric 408
Curvature, formalism of Riemann tensor proof of tensor character 276
Curvature, formalism of Riemann tensor relation to curvature 2-form 352
Curvature, formalism of Riemann tensor relation to curvature operator 274ff
Curvature, formalism of Riemann tensor relation to noncommuting covariant derivatives 389ff
Curvature, formalism of Riemann tensor Riemann, matrix display of components of 360f
Curvature, formalism of Riemann tensor spinor representation of 1154f
Curvature, formalism of Riemann tensor symmetries of 35 220ff 286 324f
Curvature, formalism of Riemann tensor wave equation for 382
Curvature, formalism of Riemann tensor, double dual of 325f 343 371 376
Curvature, formalism of scalar curvature for a 3-surface 422f
Curvature, formalism of scalar curvature Gauss — Bonnet integral of 309 381
Curvature, formalism of scalar curvature in Hilbert action principle 418 491
Curvature, formalism of scalar curvature in terms of area deficit 516
Curvature, formalism of scalar curvature introduced 222 325
Curvature, formalism of Weyl tensor see “Conformal tensor”
Curvature, formalism of York’s curvature 541 550
Curvature, methods of calculating analytical, on a computer 342
Curvature, methods of calculating geodesic Lagrangian method 344—348
Curvature, methods of calculating in extensor Chap 14
Curvature, methods of calculating mixed components of Einstein expressed explicitly in terms of Riemann components 343f
Curvature, methods of calculating straightforward method, from connection and its derivative 340f
Curvature, methods of calculating via 2-forms, method 354—362
Curvature, methods of calculating via 2-forms, theory 348—354
Curvature, methods of calculating ways to display results 334 360f
Curve, in context of differential topology 226
Curves, congruence of 240
Cutoff, related to Planck length 428
Cycloidal motion for radial geodesies m Schwarzschild geometry 664
Cycloidal motion for radius of closed Friedmann cosmology 708
Cycloidal motion for surface of a pressure-free collapsing star 852
Cycloidal motion for test particle in field of a Newtonian point mass 708
Day, length of 23—26 1124f
de Broglie wave 53 55—59
de Rham operator see “Wave operators”
de Sitter universe 745 758
Deceleration parameter of universe denned 772
Deceleration parameter of universe determinant of whether universe will recontract 774
Deceleration parameter of universe magnitude-redshift relation for measuring 782—785 794
Deceleration parameter of universe observational data on 785 788—791
Deceleration parameter of universe relationship to other cosmological parameters 771—773
Deficit angles 309 1167ff
Deflection of light, gravitational, calculated in linearized theory 184f 446
Deflection of light, gravitational, calculated in PPN formalism 1101ff
Deflection of light, gravitational, calculated in Schwarzschild coordinates 679
Deflection of light, gravitational, early Einstein words on 431
Deflection of light, gravitational, experimental results on 1104f
Deflection of light, gravitational, in flat-space theories of gravity 179 184f
Deflection of light, gravitational, magnitude of compared with current technology 1048 1101
Deflection of light, gravitational, pictorial explanation of 32
Deflection of light, gravitational, post-post-Newtonian corrections to 1069
Deflection of particles by a central field 671 1099f
Degenerate electron gas see “White-dwarf matter”
Degenerate neutron gas see “Neutron-star matter”
Degrees of freedom, counting of for geometrodynamics and electrodynamics 529—533
Delta function, Dirac 121
Delta, Kronecker 22
Democracy of histories 418—419
Density of universe (see under “Cosmology: observed properties of the universe”)
Derivative, following fluid 153 1078
Detailed balance, principle of 1028ff 1033 1035f
Determinant and Jacobian 160—161
Determinant derivative of 160—161
Deviation, geodesic see “Geodesic deviation”
DeWitt equation 1189 (see also “Emstem — Schroedmger equation”
Dicke — Brans — Jordan theory of gravity (See under “Gravitation theories
Dicke — Eotvos experiment See “Eoetvos — Dicke experiment”
Dicke’s framework for analyzing experiments 1049 1064
Differentiable manifold see “Manifold differentiable”
Differentiable structure 242
Differential conservation law, equivalence to integral conservation law 146
Differential forms see “Forms differential”
Differential geometry applications of, listed 198 (see also “Differential topology” “Affine “Riemannian and such “Connection” “Forms”)
Differential geometry Cartan’s contributions to 198
Differential geometry overview of 194—198
Differential geometry texts on 196
Differential geometry three levels of: pictorial, abstract, components 198—200
Differential geometry track-1 treatment of Chap. 8
Differential geometry track-2 treatment of Chaps. 9—11 13—15
Differential topology 197f Chap. esp “Lie
Dimensionality 10 12
Dirac brackets 486 520
Dirac delta function 121
Dirac equation, in Schwarzschild geometry 1165
Directional derivative as a tangent vector 227—230
Directional derivative of a function along a vector 59—60
Directional derivative operator for 61
Disks, rapidly rotating, in general relativity 621
Dispersion relations obtained from Hamiltonians 486f 494 498
Distance proper see “Interval Lorentz”
Distance-redshift relation (see under “Cosmology: observational probes of standard model”)
Distances, as raw material of metric 306—309
Distant action see “Action at a distance”
Distant stars, inertial influence of. see “Mach’s principle”
distribution see “Dirac delta function”
Distribution function 583f 590
Divergence of a vector or tensor 82 213 222 261
Divergences, in theory of particles and fields 426—428
Double star see “Binary star”
Dragging of inertial frames by a slowly rotating star 699
Dragging of inertial frames by Earth’s rotation 1119f
Dragging of inertial frames in Kerr — Newman geometry 879ff 893—896
Dragging of inertial frames in PPN formalism 1117—1120
Dragging of inertial frames prospects to measure 1120 (see also “Mach’s principle”)
Dual bases 60f 119 202 232
Duality operation on forms, vectors, and tensors application to electromagnetism 88 97f 114
Duality operation on forms, vectors, and tensors double dual of Riemann 371 376
Duality operation on forms, vectors, and tensors not to be confused with duality of bases 119
Duality operation on forms, vectors, and tensors on forms 88 97f 108 119 151
Duality operation on forms, vectors, and tensors on simple forms, expressed in terms of perpendicularity 98
Duality operation on forms, vectors, and tensors special star operation that does not act on forms 376—380
Duality rotation of electromagnetic field 108 482f
Dynamical path length as proportional to phase of wave function 486
| Dynamical path length in elementary mechanics 486—487
Dynamical path length in superspace formulation of geometrodynamics 419 1186
d’Alembertian operator see “Wave operators”
Earth atmosphere and gravity 388
Earth crust, as detector of gravitational waves 1013 1015
Earth general precession (precession of rotation axis) 391 392 1112 1113
Earth gravitational multipole moments 401
Earth mass, radius, density see “Endpapers”
Earth motion relative to cosmic microwave radiation 713
Earth particles oscillating in hole bored through 39
Earth rotation of, drags inertial frames 1119f (see also “Day”)
Earth satellite orbits used to deduce mass 638
Earth shape as described by collection of distances 306—309
Earth subsurface mass variations 401
Earth tides, as experimental test of general relativity 1123f
Earth vibrations of, as detector for gravitational waves 1013 1015 1035f
Eccentricity of an elliptical orbit 647
Eclipses 24—26 1104
Eddington — Finklestein coordinates 828—831 849
Eddington — Finklestein diagrams 829 830 849 864 873
Effective potentials (continued) for charged test particles in equatorial plane of Kerr — Newman hole 911
Effective potentials for oscillations of mixmaster universe 809ff
Effective potentials for radius of Friedmann universe 706 744 746 748f
Effective potentials for scalar waves in Kerr geometry 915
Effective potentials for test particles in Schwarzschild geometry 639 656 659—662
Effective potentials for waves in Schwarzschild geometry 868 870
Eikonal method 1102
Einstein (see under “Curvature formalism
Einstein A coefficients 1029
Einstein field equation 431—434
Einstein field equation and collapse 1198—1199 (see also “Geometrodynamics”)
Einstein field equation correspondence with Newtonian theory 412—416
Einstein field equation derivations of from automatic conservation of source 379f 417
Einstein field equation derivations of from Hilbert’s action principle 418
Einstein field equation derivations of from physics on a spacelike slice 419—423
Einstein field equation derivations of from spin-2 field theory 424f 437
Einstein field equation derivations of from superspace analysis 423f
Einstein field equation derivations of from “metric elasticity of space” 426ff
Einstein field equation derivations of in extensor Chap 17 esp. 416—482
Einstein field equation elementary introduction to 41ff
Einstein field equation integral equation equivalent to 995—996
Einstein field equation modified by cosmological term 410—412
Einstein field equation variational principles for (see under “Variational principles”
Einstein static universe 746 747 750 758f
Einstein summation convention 9
Einstein tensor (see under “Curvature formalism
Einstein — Infeld — Hoffman equations of motion 1091 1094—1095
Einstein — Rosen bridge 837ff
Einstein — Schrodinger equation 1189f
Einstein’s elevator 298 (see also “Equivalence principle”)
Einstein’s theory of gravity see “General relativity”
Elasticity 426—428
Electrodynamics analog of Palatini variational method in 495—498
Electrodynamics analogies and comparisons with geometrodynamics 35 348 364 367—370 “Integrating
Electrodynamics canonical formulation of, as a guide to geometrodynamics 496f 522ff
Electrodynamics deduced from electrostatics plus covariance 81
Electrodynamics deduced from vector potential 122
Electrodynamics in curved spacetime, in extenso 385—391 568—570
Electrodynamics in flat spacetime, in extensor Chap 3
Electrodynamics in geometric optics limit see «Geometric optics”
Electrodynamics in language of forms, in extensor Chap 4
Electrodynamics in language of spinors 1154 1165
Electrodynamics in terms of boundary of a boundary 365—370
Electrodynamics lines of force never end as core principle of 420
Electrodynamics three-plus-one view versus geometric view 78—79
Electromagnetic field calumoid 125
Electromagnetic field complexion 108 482
Electromagnetic field descriptions of and equations governing electric and magnetic fields 73f
Electromagnetic field divergence vanishes 89
Electromagnetic field dual of electromagnetic field tensor Maxwell divergence vanishes 88
Electromagnetic field dual of electromagnetic field tensor Maxwell egg-crate picture of 107 109
Electromagnetic field dual of electromagnetic field tensor Maxwell exterior derivative gives charge density and current 113f
Electromagnetic field dual of electromagnetic field tensor Maxwell introduced 88 105
Electromagnetic field electromagnetic field tensor (or 2-form), Faraday as machinery to produce force from 4-velocity 73 101 104
Electromagnetic field electromagnetic field tensor (or 2-form), Faraday components of 73—74
Electromagnetic field electromagnetic field tensor (or 2-form), Faraday divergence gives charge density and current 81 88
Electromagnetic field electromagnetic field tensor (or 2-form), Faraday egg-crate pictures of 99f 104 106 107 111
Electromagnetic field electromagnetic field tensor (or 2-form), Faraday expressed in terms of exterior products 99
Electromagnetic field electromagnetic field tensor (or 2-form), Faraday exterior derivative vanishes 112f 117
Electromagnetic field electromagnetic field tensor (or 2-form), Faraday generic case reduced to simplest form 122 483
Electromagnetic field electromagnetic field tensor (or 2-form), Faraday Maxwell’s equations for, in component notation 80f 568
Electromagnetic field electromagnetic field tensor (or 2-form), Faraday special cases of pure electric, pure magnetic, and null 122
Electromagnetic field electromagnetic field tensor (or 2-form), Faraday “canonical representation” of 122
Electromagnetic field field momentum 496f 522ff
Electromagnetic field invariants 110 480—483
Electromagnetic field Lorentz force 71ff 101 104 568
Electromagnetic field Lorentz transformation of 78f
Electromagnetic field Lorentz transformations 78f 108ff 482f
Electromagnetic field Maxwell’s equations 80f 568
Electromagnetic field produced by specific sources oscillating dipole 111—112
Electromagnetic field produced by specific sources point charge 107—111 121f
Electromagnetic field stress-energy tensor 140f
Electromagnetic field vector potential 88f 120 569
Electromagnetic field vector potential wave equation for 89 120 388—391 569
Electron capture, in white-dwarf matter 619
Electron quasibound in field of small black hole 1164
Electron spinning, Thomas precession of 175—176
Elementary-particle experiments as tests of relativity theory 1054f 1060 energymomentum”)
Elements, abundances of 765
Elevator 431 (see also “Uniqueness of free fall” “Tide-producing
ElH equations of motion 1091 1094—1095
Embedding diagrams for a spherical, collapsing star 855—856
Embedding diagrams for a static, spherical star 613—615 617
Embedding diagrams for Friedmann cosmological models 723 725
Embedding diagrams for Schwarzschild geometry 837 839 528
Embedding diagrams general discussion 613
Energy in mechanics, as time rate of change of action 486—487
Energy-at-infinity in Kerr — Newman geometry 898f 910
Energy-at-infinity in Schwarzschild geometry 656ff
Energy-momentum 4-vector 51 53f 68
Energy-momentum conservation of (see under “Conservation laws”)
Energy-momentum density of 3-form for 151
Energy-momentum density of revealed by stress-energy tensor 131
Energy-momentum Four-vector see “Vector”
Energy-momentum of gravitational field nonlocalizable in generic case 466ff
Energy-momentum of gravitational localizable only to within a wavelength for gravitational waves 955f 964—966 969f
Energy-momentum of gravitational precisely localizable only for spherical systems 603—604 858f
Energy-momentum total, of a gravitating source expressed as a flux integral 461—464
Energy-momentum total, of a gravitating source expressed as a volume integral 464—466
Energy-momentum total, of a gravitating source in terms of asymptotic gravitational field Chap 19
entropy (see under “Second law of thermodynamics”)
Eoetoes — Dicke experiments 14—17 1050—1055
Eoetoes — Dicke experiments early Einstein words on 431
Eoetoes — Dicke experiments for massive (self-gravitating) bodies 1127—1131
Eoetoes — Dicke experiments implications for constancy of fundamental constants 1061—1063
Ephemeris for solar system (J.P.L.) 1095 1097
Ephemeris second 28
Equation of structure, Cartan’s 378
Equations of motion derived from Einstein field equation 42—43 471—480
Equations of motion for bodies separated by distances large compared to their sizes deviations from geodesic motion 1120—1121 1128
Equations of motion for bodies separated by distances large compared to their sizes “EIH” (post-Newtonian) for spherical bodies 1091 1094—1095
Equations of state for nuclear and white-dwarf matter 624—626
Equations of state for “cosmological fluid” 713 726
Equinoxes, precession of 391f 1112f
Equivalence principle basis for affine parameter 211 250
Equivalence principle bridge from special relativity to general relativity 164 Chap 207
Equivalence principle Einstein’s 1911
Equivalence principle enunciated 386f 1060
Equivalence principle factor-ordering problems m 388—391
Equivalence principle formulation of 17
Equivalence principle in Newton — Cartan theory 297
Equivalence principle out of spin-2 field theory 425
Equivalence principle role in metric theories 1067f
Equivalence principle tests of 187—190 1054—1063
Equivalence principle weak equivalence principle see “Uniqueness of free fall”
Ergosphere 880
Ether 1051 1064f
Euclidean geometry 19—22
Euclidean geometry contrasted with Lorentz geometry 51
Euler equation of hydrodynamics applied to a collapsing star 858
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