Misner C.W., Thorne K.S., Wheeler J.A. — Gravitation :: Электронная библиотека попечительского совета мехмата МГУ

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Misner C.W., Thorne K.S., Wheeler J.A. — Gravitation

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Название: Gravitation

Авторы: Misner C.W., Thorne K.S., Wheeler J.A.

Аннотация:

Put as simply as possible, this is a book on Einstein's theory of gravity (general relativity). It is the first textbook on the subject that uses throughout the modern formalism and notation of differential geometry, and it is the first book to document in full the revolutionary techniques developed during the past decade to test the theory of general relativity.

Язык:

Рубрика: Физика/Гравитационное взаимодействие/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1971

Количество страниц: 1278

Добавлена в каталог: 22.09.2005

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Предметный указатель

Radio sources, cosmic      759—762
Radio sources, cosmic isoiropy on sky      703 (see also “Quasars”)
Radius of closed Friedmann universe      704f
Raising indices      see “Index manipulations”
Rays, in geometric optics      573ff 581f
Redshift Doppler      63f 794
Redshift due to “ether drift”      1064f
Redshift of radiation from a collapsing star      847 849f 872
Redshift parameter, z, denned      187
Redshift, cosmological contrasted with Doppler shift      794
Redshift, cosmological derivations from standing waves      776
Redshift, cosmological derivations from wave-crest emission, propagation, and reception      777f
Redshift, cosmological derivations using symmetry-induced constant of geodesic motion      777 780
Redshift, cosmological in anisotropic cosmology      801 (see also under “Cosmology”)
Redshift, cosmological independent of wavelength      775
Redshift, cosmological of cosmic microwave radiation      764—765 779
Redshift, cosmological of particle energies and de Broglie waves      780
Redshift, cosmological used to characterize distances and times in universe      779
Redshift, cosmological “tired light” does not explain      775
Redshift, gravitational, for gravitational waves      956f 968
Redshift, gravitational, for photons compared with 1970 clock technology      1048
Redshift, gravitational, for photons derivation from energy conservation      187
Redshift, gravitational, for photons equivalence principle tested by      189f 1056
Redshift, gravitational, for photons experimental results      1058 1060
Redshift, gravitational, for photons from geodesic equation in generic static metric      657 659
Redshift, gravitational, for photons geodesic motion tested by      1055—1060
Redshift, gravitational, for photons implies spacetime is curved      187—189
Redshift, gravitational, for photons in linearized theory      446f
Redshift, gravitational, for photons in solar spectum      1058—1060
Redshift, gravitational, for photons Pound — Rebka-Snider experiment      1056—1058
Redshift, gravitational, for temperature      568 685
Reference system      see “Coordinate system” “Inertial “Lorentz “Proper
Regge calculus, applications and future of      1178—1179
Regge calculus, blocks associated with one hinge      1170
Regge calculus, choice of edge lengths      1177—1178
Regge calculus, choice of lattice structure      1173—1177
Regge calculus, continuum limit of      1169
Regge calculus, count of faces      1177
Regge calculus, Einstein’s geometrodynamic law, expressed in      1173
Regge calculus, facing, packing, and right-through blocks      1176
Regge calculus, flow diagram for      1171—1172
Regge calculus, geometry determined by lengths      1167
Regge calculus, hinges      1169
Regge calculus, initial-value data in      1172
Regge calculus, simplexes and deficit angles      1167—1169
Regge calculus, skeleton geometry      1169
Regge calculus, suitable for low-symmetry geometrodynamics      1166
Regge calculus, supplementary vertices in      1176
Regge calculus, surveyed      Chap. 42
Regge calculus, variational principle for geometrodynamics      1170
Regge — Wheeler radial coordinate      see “Tortoise coordinate”
Reissner — Nordstram geometry as limiting case of Kerr — Newman      878
Reissner — Nordstram geometry coordinates with infinity conformally transformed      920
Reissner — Nordstram geometry derivation of metric      840—841
Reissner — Nordstram geometry global structure of      920—921
Reissner — Nordstram geometry Kruskal-like coordinates for      841
Reissner — Nordstram geometry throat for Q = M identical to Bertoiti — Robinson universe      845
Reissner — Nordstram geometry uniqueness of (Birkhoff-iype theorem)      844ff
Relative acceleration      see “Geodesic deviation”
Relativity      see “Special relativity”; “General relativity”
Renormalization of zero-point energy of particles and fields      426ff
Retarded fields and radiation reaction      474
Retarded potential      121
Reversible and irreversible transformations in black-hole physics      889f
Ricci curvature      see under “Curvature formalism
Ricci rotation 1-forms      see «Rotation 1-forms”
Ricci rotation coefficients      see “Connection coefficients”
Riemann      see under “Curvature formalism
Riemann normal coordinates      285ff 480—486
Riemannian geometry characterized      242 304f
Riemannian geometry of apple, is locally Euclidean      19—21
Riemannian geometry of spacetime, is locally Lorentzian      19—23 (see also specific concepts such “Connection”)
Riemannian geometry Riemann’s founding of      220
Riemannian geometry track-1 treatment of      Chap. 8
Riemannian geometry track-2 treatment of      Chap. 13
Robertson — Walker line element      722 759
Rods      301 393 396—399
Roll — Krotkov — Dicke experiment      see “Eotvos — Dicke experiments”
Rotation 1-forms $\omega^{\mu}{}_{\nu}$       350—354 360
Rotation 1-forms $\omega^{\mu}{}_{\nu}$ matrix notation for      359 (see also “Covariant derivative” “Connection
Rotation as stabilizer of stars      633f
Rotation group SO(3), manifold of generators      242—243 264
Rotation group SO(3), manifold of geodesies and connection      264 332
Rotation group SO(3), manifold of isometric to 3-sphere      725
Rotation group SO(3), manifold of metric      332
Rotation group SO(3), manifold of Riemann curvature      288
Rotation group SO(3), manifold of structure constants      243 332
Rotation group SO(3), manifold of used in constructing mixmaster cosmological model      807
Rotation matrices      see “Spin matrices”
Rotation of universe, limits on      939
Rotation operators      see “Spin matrices”
Rotation rigid-body      123f
Rotations composition of      1135—1138
Rotations half-angles arise from reflections      1137
Rotations in coordinate plane      67
Rotations infinitesimal      170f 1140ff
Rotations represented as two reflections      1137ff
Rotations Rodrigues formula      1137
Rutherford scattering      647 669
Rutherford scattering relativistic corrections to      669f
Saddle points, number of      318
Sakharov view of gravitation      426—428
Scalar field equation of motion, from Einstein’s field equation      483
Scalar field propagation in Schwarzschild geometry      863 868ff
Scalar field stress-energy tensor      483
Scalar product of vectors      22 52f 62
Scalar-tensor theories of gravity      see under “Gravitation theories
Schild’s argument for curvature      187—189
Schild’s ladder, applications      251—253 258 263 268 278
Schild’s ladder, described      249
Schwarzschild coordinates for a pulsating star      689
Schwarzschild coordinates for any static, spherical system      597
Schwarzschild coordinates for Schwareschild geometry      607
Schwarzschild coordinates pathology at gravitational radius      11 823—826
Schwarzschild geometry      822
Schwarzschild geometry applications as exterior of a collapsing star      846—850
Schwarzschild geometry applications as external field of a static star      607
Schwarzschild geometry applications many Schwarzschild solutions joined in lattice to form closed universe      739f
Schwarzschild geometry applications matched to Friedmann geometry to produce model for collapsing star      851ff
Schwarzschild geometry as limiting case of Kerr — Newman      878
Schwarzschild geometry BirkhofTs theorem for      843—844
Schwarzschild geometry coordinate systems and reference frames coordinates with infinity conformally transformed      919f
Schwarzschild geometry coordinate systems and reference frames ingoing Eddington — Finklestein coordinates      312 828f 849
Schwarzschild geometry coordinate systems and reference frames isotropic coordinates      840
Schwarzschild geometry coordinate systems and reference frames Kruskal — Szekeres coordinates      827 831—836
Schwarzschild geometry coordinate systems and reference frames Novikov coordinates      826—827
Schwarzschild geometry coordinate systems and reference frames orthonormal frames      821
Schwarzschild geometry coordinate systems and reference frames outgoing Eddington — Finklestein coordinates      829ff
Schwarzschild geometry coordinate systems and reference frames Schwarzschild coordinates      607 823—826
Schwarzschild geometry coordinate systems and reference frames tortoise coordinate      663 665f
Schwarzschild geometry derivation from full field equations      607
Schwarzschild geometry derivation from initial-value equation      538
Schwarzschild geometry destruction of all particles that fall inside gravitational radius      836 839 860—862
Schwarzschild geometry Dirac equation in      1164
Schwarzschild geometry explored by radially infalling observer      820—823
Schwarzschild geometry in extens      Chaps 25 31
Schwarzschild geometry perturbations of high-frequency, analyzed by geometric optics      640
Schwarzschild geometry perturbations of stability against small      884
Schwarzschild geometry perturbations of wave equations for, related to Hamilton — Jacobi equation      640
Schwarzschild geometry photon motion in capture cross section      679
Schwarzschild geometry photon motion in critical impact parameter for capture      673
Schwarzschild geometry photon motion in effective potential for radial part of motion      673f 676
Schwarzschild geometry photon motion in escape versus capture as a function of propagation direction      675
Schwarzschild geometry photon motion in impact parameter      672
Schwarzschild geometry photon motion in qualitative description of      674f
Schwarzschild geometry photon motion in scattering cross section      676—679
Schwarzschild geometry photon motion in shape of orbit      673 677
Schwarzschild geometry Riemann curvature      821ff
Schwarzschild geometry Riemann curvature structure and evolution Einstein — Rosen bridge (wormhole)      837ff 842f
Schwarzschild geometry Riemann curvature structure and evolution evolution      838ff 842

Schwarzschild geometry Riemann curvature structure and evolution not static inside gravitational radius      838
Schwarzschild geometry Riemann curvature structure and evolution Riemann curvature structure and evolution diagram of causal structure      920
Schwarzschild geometry Riemann curvature structure and evolution Riemann curvature structure and evolution embedding diagrams      528 837 839
Schwarzschild geometry Riemann curvature structure and evolution Riemann curvature structure and evolution singularities      see “Singularities of Schwarzschild geometry”
Schwarzschild geometry Riemann curvature structure and evolution Riemann curvature structure and evolution singularities at r = 0      see under “Singularities”
Schwarzschild geometry Riemann curvature structure and evolution topology      838ff
Schwarzschild geometry test-particle motion in analyzed using Hamilton — Jacobi theory      649
Schwarzschild geometry test-particle motion in analyzed using symmetry-induced constants of the motion      656—672
Schwarzschild geometry test-particle motion in angular momentum      656ff
Schwarzschild geometry test-particle motion in binding energy of last stable circular orbit      885 911
Schwarzschild geometry test-particle motion in circular orbits, stability of      662
Schwarzschild geometry test-particle motion in conserved quantities for      656
Schwarzschild geometry test-particle motion in deflection angle      671
Schwarzschild geometry test-particle motion in effective potential for radial part of motion      639 656 659—662
Schwarzschild geometry test-particle motion in energy-at-infinity      656ff
Schwarzschild geometry test-particle motion in extensor      Chap. 25
Schwarzschild geometry test-particle motion in nonradial orbits, details of      668
Schwarzschild geometry test-particle motion in orbit lies in a “plane”      645f 655
Schwarzschild geometry test-particle motion in periastron shift for nearly circular orbits      670
Schwarzschild geometry test-particle motion in qualitative description of orbits      662
Schwarzschild geometry test-particle motion in radial orbits, details of      663—668 820—823 824—826 835
Schwarzschild geometry test-particle motion in scattering cross section      669f
Schwarzschild geometry wave propagation in effective potentials for      868 870
Schwarzschild geometry wave propagation in electromagnetic field, Newman — Penrose constants      870f
Schwarzschild geometry wave propagation in fields of zero rest mass, integer spin      866
Schwarzschild geometry wave propagation in scalar field, analyzed in detail      863 868ff
Schwarzschild lattice universe      739f
Schwarzschild radius      see “Gravitational radius”
Schwarzschild surface      see “Gravitational radius”
Schwarzschild’s uniform-density stellar model      609—612
Second law of black-hole dynamics      931ff
Second law of black-hole dynamics formulated with assumptions ignored      889 891
Second law of black-hole dynamics reversible and irreversible transformations      889f 907—910 913
Second law of black-hole dynamics used to place limits on gravitational waves from hole-hole collisions      886
Second law of thermodynamics      563 567f
Second moment of mass distribution, defined      977
Second, changing definitions of      23—29
Selector parameter defined      265—266
Selector parameter used in analysis of geodesic deviation      Chap. 11
Semicolon notation for covariant derivative      210
Semimajor axis of an elliptic orbit      647
Separation vector      29ff 218f 265—270
Shear stress idealized away for perfect fluid      140
Shear stress in PPN formalism      1074 1075n
Shear stress produced by viscosity      567
Shell crossing      859
Shift function as Lagrange multiplier      487
Shift function award of arbitrariness in, reversed      532
Shift function covariant and contravariant forms of      507f
Shift function metric interval as fixed by      507
Shift function two variational principles for      538
Shock waves hydrodynamic      559 564 628
Shock waves in spacetime curvature      554
Signals, extraction of from noise      1036—1038
Signature, of metric      311
Simple fluid, defined      558
simplex      307 38Of 1167ff
Simultaneity as term for spacelike slice      see “Spacelike slice”
Simultaneity in Newion, Minkowskii, and Einstein spacetime      296
Singularities in geometry of spacetime and spherical gravitational collapse of a star      846 860ff
Singularities in geometry of spacetime cosmic censorship vs. naked singularities      937
Singularities in geometry of spacetime definitions of      934
Singularities in geometry of spacetime in Schwarzschild geometry, and evolution of the geometry      838f
Singularities in geometry of spacetime Mixmaster      805—813
Singularities in geometry of spacetime Mixmaster changing standards of time near      813f
Singularities in geometry of spacetime Mixmaster initial, of the universe      769f
Singularities in geometry of spacetime Mixmaster initial, of the universe prospects for understanding      707
Singularities in geometry of spacetime Mixmaster initial, of the universe what “preceded” it      769f
Singularities in geometry of spacetime Mixmaster is generic      806 940
Singularities in geometry of spacetime Mixmaster should one worry about singularities Misner’s viewpoint      813f
Singularities in geometry of spacetime Mixmaster should one worry about singularities Thome’s neutrality      1010f
Singularities in geometry of spacetime Mixmaster should one worry about singularities Wheeler’s viewpoint      1196ff
Singularities in geometry of spacetime Mixmaster unphysical, due to overidealization shell crossings      859
Singularities in geometry of spacetime Mixmaster unphysical, due to overidealization surface layers      552—556
Singularities in geometry of spacetime remote possibility that infalling objects might destroy      840
Singularities in geometry of spacetime structures of      935 940 804ff
Singularities in geometry of spacetime theorems on creation of      934ff 936 938 762
Singularities, coordinate      10—12
Singularities, coordinate illustrated by Schwarzschild coordinates      11 823ff
Size of accelerated frame      168f
Size related to angular momentum      162
Skeleton geometry      309 1169
Skeleton history      499
Slicing of spacetime      506 (see also “Spacelike slice”)
Solar system      752—756
Solar system ephemeris for (J.P.L.)      1095 1097
Solar system Nordtvedt effect in      1128 (see also “Earth” “Moon” “Planetary “Sun” “Experimental
Solar system relativistic effects in, magnitude of      1048 1068
Source counts in cosmology      798
Space foamlike structure and quantum fluctuations      1204
Space Newtonian absolute      19 40 291f
Space not spacetime, as the dynamic object      1181 (see also “Manifold” Differential “Differential “Affine “Riemannian
Space theory of matter      1202—1205
Spacecraft, used to test general relativity      1108f 1114
Spacelike slice as the dynamic object in superspace      423f 1181
Spacelike slice as “moment of time’ in spacetime      713f
Spacelike slice geometrodynamics and electrodynamics derived from physics on      419—423 (see also “Embedding diagrams” “Initial “Three-geometries”
Spacetime geometry Ensteinian as classical approximation      1181f
Spacetime geometry Ensteinian as classical leaf slicing through superspace      1184 (see also “General Relativity” “Geometrodynamics” “Curvature
Spacetime geometry Ensteinian as dynamic participant in physics      337
Spacetime geometry Ensteinian curvature of implied by gravitational red shift      187ff
Spacetime geometry Ensteinian modeled by apple, 4 Riemannian character tested by stability of Earth      398f
Spacetime geometry Ensteinian response to matter, as heart of general relativity      404
Spacetime geometry Ensteinian stratification denied by locally Lorentz character of physics      304f
Spacetime geometry Ensteinian viewed as a “gravitational field”      399f
Spacetime geometry Minkowskiian (Loreniz)      see «Lorentz geometry”
Spacetime geometry Newtonian      see “Newton — Cartan theory of gravity”
Spacetime geometry Newtonian, Minkowskiian and Einsteinian, compared and contrasted      296 437
Special relativity briefly outlined      47—48
Special relativity does not take in gravitation      Chap. 7
Special relativity local validity as central feature of curved spacetime      304f (see also specific concepts e.g. “Electromagnetic “Lorentz
Special relativity spelled out      Chaps. 2—6
Specific flux, defined      1025
Specific intensity, denned      587 589
Sphere 2-dimensional metric on      340
Sphere 2-dimensional Riemann tensor of      341
Sphere 2-dimensional topology of      241f
Sphere 2-dimensional two coordinate patches to cover      12
Sphere 3-dimensional compared with spheres of lower dimensionality      704
Sphere 3-dimensional embedding diagram      723
Sphere 3-dimensional hyperspherical coordinates and metric for      723f
Sphere 3-dimensional isometric to manifold of rotation group      725
Sphere 3-dimensional Riemann curvature tensor      721
Sphere 3-dimensional volume of      724
Spherical symmetry, Killing vectors for      658
Spherical systems, dynamic Birkhoff’s theorem for      883f
Spherical systems, dynamic curvature tensors for      361f
Spherical systems, dynamic Schwarzschild coordinates for      616f 689
Spherical systems, static curvature tensors for      360f
Spherical systems, static isotropic coordinates for      595
Spherical systems, static orthonormal frames for      598
Spherical systems, static rigorous derivation of line element      616f
Spherical systems, static Schwarzschild coordinates for      594—597
Spin matrices algebraic properties      1137—1142
Spin matrices and 3-vectors      1140f
Spin matrices and 4-vectors      1142f
Spin matrices as quaternions or rotation operators      1136
Spin matrices associated spin matrices      1152f
Spin matrices Hermitian conjugate of      1138
Spin matrices in law of combination of rotations      1136
Spin matrices multiplication law for      1153
Spin, as nonclassical two-valuedness      1204
Spindown of black holes      886
Spinning body equation of motion for      1120f
Spinning body spin precessions due to space curvature (“geodetic’)      1119f
Spinning body spin precessions frame-dragging      1119f
Spinning body spin precessions Thomas      175f 1118 1145ff
Spinning body spin precessions “general”      391f
Spinning body transport law for spin Fermi — Walker, in absence of curvature coupling      165 176f 1117
Spinning body transport law for spin modified by curvature coupling      391f

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