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

Isotropy implies homogeneity      715 723
Jacobi identity, for commutators      240
Jacobian      93 148 160f
Jacob’s ladder      see “Schild’s ladder”
Jeans instability      757
Junction conditions      490
Junction conditions across null surface      554
Junction conditions and motion of surface layer      555
Junction conditions applied to collapsing shell of dust      555—556
Junction conditions applied to surface of a collapsing star      852—853
Junction conditions extrinsic curvature may jump      554
Junction conditions from electrodynamics as guide      551
Junction conditions intrinsic geometry continuous      553
Junction conditions relevant components of Einstein field equation      552
Junction conditions surface stress-energy tensor      552—553
Jupiter, motion of satellites      637
Kasner cosmological model      801 805ff
Keplerian orbits in Newtonian field of a point mass      647—649
Keplerian orbits in Newtonian field of a point mass analyzed using Hamilton — Jacobi theory      644—649
Keplerian orbits in Newtonian field of a point mass effective potential for      661
Kepler’s laws, discovery by Kepler      755
Kepler’s laws, “1-2-3” law      39 450 457
Kernel, of wave operator      121
Kerr coordinates      879f
Kerr diagram      881
Kerr geometry, as limiting case of Kerr — Newman      878
Kerr — Newman geometry and electromagnetic field Boyer — Lindquist coordinates electromagnetic field tensor      877 878
Kerr — Newman geometry and electromagnetic field Boyer — Lindquist coordinates metric      877 878
Kerr — Newman geometry and electromagnetic field Boyer — Lindquist coordinates pathology of at horizon      880
Kerr — Newman geometry and electromagnetic field Boyer — Lindquist coordinates vector potential      898
Kerr — Newman geometry and electromagnetic field dynamic properties change of M, Q, S when particles fall into horizon      904—910 913
Kerr — Newman geometry and electromagnetic field dynamic properties electromagnetic energy of      890
Kerr — Newman geometry and electromagnetic field dynamic properties irreducible mass      889—890 913
Kerr — Newman geometry and electromagnetic field dynamic properties reversible and irreversible transformations of      889—890
Kerr — Newman geometry and electromagnetic field dynamic properties role as endpoint of gravitational collapse      882—883
Kerr — Newman geometry and electromagnetic field dynamic properties rotational energy of      890
Kerr — Newman geometry and electromagnetic field dynamic properties stability against small perturbations      884—885
Kerr — Newman geometry and electromagnetic field history of      877n
Kerr — Newman geometry and electromagnetic field horizon      879ff
Kerr — Newman geometry and electromagnetic field horizon angular velocity of      914
Kerr — Newman geometry and electromagnetic field horizon area of      889 914
Kerr — Newman geometry and electromagnetic field horizon null generators of      903—904
Kerr — Newman geometry and electromagnetic field Kerr coordinates electromagnetic field tensor      879
Kerr — Newman geometry and electromagnetic field Kerr coordinates metric      879
Kerr — Newman geometry and electromagnetic field Kerr coordinates transformation between Kerr and Boyer — Lindquist coordinates      879f
Kerr — Newman geometry and electromagnetic field Kerr diagram for      881
Kerr — Newman geometry and electromagnetic field Kerr — Schild coordinates      903
Kerr — Newman geometry and electromagnetic field Killing tensor      893
Kerr — Newman geometry and electromagnetic field Killing tensor principal null congruences      901—904
Kerr — Newman geometry and electromagnetic field Killing vectors      879 892ff
Kerr — Newman geometry and electromagnetic field light cones      891 896—897
Kerr — Newman geometry and electromagnetic field light cones electromagnetic-field structure      877ff 883 892
Kerr — Newman geometry and electromagnetic field limiting cases (Schwarzschild, Reissner — Nordstram, Kerr, extreme Kerr — Newman)      878
Kerr — Newman geometry and electromagnetic field locally nonrotating observers      895—896
Kerr — Newman geometry and electromagnetic field magnetic dipole moment      883 892
Kerr — Newman geometry and electromagnetic field maximal analytic extension of      882
Kerr — Newman geometry and electromagnetic field multipole moments of      883 892
Kerr — Newman geometry and electromagnetic field parameters of (M, Q, S, or a)      878
Kerr — Newman geometry and electromagnetic field rotational properties dragging of inertial frames      879ff 893—896
Kerr — Newman geometry and electromagnetic field rotational properties ergosphere      880
Kerr — Newman geometry and electromagnetic field rotational properties gyromagnetic ratio      883 892
Kerr — Newman geometry and electromagnetic field rotational properties intrinsic angular momentum vector      891
Kerr — Newman geometry and electromagnetic field rotational properties static limit      879ff 894
Kerr — Newman geometry and electromagnetic field stationary observers      893—894
Kerr — Newman geometry and electromagnetic field test-particle motion in axial component of angular momentum      898—899
Kerr — Newman geometry and electromagnetic field test-particle motion in binding energy of last stable circular orbit      885 911
Kerr — Newman geometry and electromagnetic field test-particle motion in Carter’s fourth constant of the motion, $\mathscr Q$ or $\mathscr K$       899
Kerr — Newman geometry and electromagnetic field test-particle motion in effective potential for equatorial motion      911
Kerr — Newman geometry and electromagnetic field test-particle motion in energy-at-inflnity      898—899 910
Kerr — Newman geometry and electromagnetic field test-particle motion in equations of motion in separated form      899—900 901
Kerr — Newman geometry and electromagnetic field test-particle motion in Hamilton — Jacobi derivation of equations of motion      900—901
Kerr — Newman geometry and electromagnetic field test-particle motion in orbits in equatorial plane      911—912
Kerr — Newman geometry and electromagnetic field test-particle motion in rest-mass of particle      899
Kerr — Newman geometry and electromagnetic field test-particle motion in super-Hamiltonian for      897
Kerr — Newman geometry and electromagnetic field uniqueness as external field of a black hole heuristic explanation of uniqueness      875 877
Kerr — Newman geometry and electromagnetic field uniqueness as external field of a black hole implications for realistic gravitational collapse      863
Kerr — Newman geometry and electromagnetic field uniqueness as external field of a black hole theorems implying uniqueness      876 938 939
Kerr — Newman geometry and electromagnetic field wave propagation in      914—915
Kerr — Schild coordinates      903
Killing tensor field      893n
Killing vector fields      650—653
Killing vector fields associated conservation laws for test-particle motion      651
Killing vector fields commutator of is Killing vector      654
Killing vector fields eigenvalue problem for finding      654
Killing vector fields for flat spacetime      654
Killing vector fields for Kerr — Newman geometry      879 892ff
Killing vector fields for spherically symmetric manifolds      658
Killing’s equation      650
Kinetic theory in curved spacetime applications      583
Kinetic theory in curved spacetime applications computation of optical appearance of a collapsing star      850
Kinetic theory in curved spacetime applications elementary expression for pressure      139—140
Kinetic theory in curved spacetime applications photons      587ff
Kinetic theory in curved spacetime applications relativistic star clusters      679—687
Kinetic theory in curved spacetime applications stress-energy tensor as integral over momentum Kinetic theory in curved spacetime applications space      589f
Kinetic theory in curved spacetime basic concepts distribution function (number density in phase space) defined      583f 590
Kinetic theory in curved spacetime basic concepts mass hyperboloid      585
Kinetic theory in curved spacetime basic concepts momentum space      583ff 590
Kinetic theory in curved spacetime basic concepts phase space      584f 590
Kinetic theory in curved spacetime basic concepts volume in phase space      584—587 590
Kinetic theory in curved spacetime basic laws collisionless Boltzmann equation (kinetic equation)      587 590
Kinetic theory in curved spacetime basic laws Liouville’s theorem for noninteracting particles in curved spacetime      584 586—587 590
Kinetic theory in curved spacetime basic laws specialized to photons      587—589
Kinetic theory in curved spacetime in extenso      583—590
Klein — Alfven cosmology      748 770
Kronecker delta      22
Kruskal diagrams      528 834f 839 848 855
Kruskal — Szekeres coordinates for metric in      827
Kruskal — Szekeres coordinates for relationship to Schwarzschild coordinates      833—835
Kruskal — Szekeres coordinates for Schwarzschild geometry      828—832
K’ai-feng observatory      11
Lagrangian perturbations      690—691
Lamb — Retherford shift, principal mechanism      1190
Landau — Lifshitz pseudotensor      see “Pseudotensor”
Laplace operator, vs. d’Alembertian      177
Lapse function as Lagrange multiplier      487
Lapse function award of arbitrariness in, reversed      532
Lapse function covariant and contra variant forms of      507—508
Lapse function metric interval as fixed by      507
Lapse function variational principle for      538
Laser ranging to moon      1048 1130f
Lattice      see “Clocks”; “Rods”
Laws of physics in curved spacetime      384—393 (see also specific laws e.g. “Kinetic “Hydrodynamics” “Conservation
Leap second      28
Least action, principle of applied in elementary Hamiltonian mechanics      125—126
Least action, principle of related to extremal time      315—324
Lens effect      589 795f 887
Levi — Civita tensor in flat spacetime      87f
Levi — Civita tensor in general basis      202 207
Levi — Civita tensor in spherical coordinates      206
Levi — Civita tensor orientation of      87f
Lie derivative independent of any affine connection      517
Lie derivative of a tensor      517
Lie derivative of a vector      240
Lie groups      198
Lie transport law      240
Light cone characterization of advanced and retarded potentials      122
Light cone Newton — Cartan vs. Einstein difference      297 (see also “Causal relationships”)
Light, bending of      see “Deflection of light”
Line element      see “Metric”
Linearized theory of gravity (same as Spin-2 theory in flat spacetime) equivalence of the two theories spelled out      435
Linearized theory of gravity (same as Spin-2 theory in flat spacetime) presentation as linearized limit of general relativity      Chap 18 448—451 461—464 944—955
Linearized theory of gravity (same as Spin-2 theory in flat spacetime) presentation as linearized limit of general relativity bar operation      436—438
Linearized theory of gravity (same as Spin-2 theory in flat spacetime) presentation as linearized limit of general relativity curvilinear coordinates      441
Linearized theory of gravity (same as Spin-2 theory in flat spacetime) presentation as linearized limit of general relativity effect of gravity on matter and photons      442—444
Linearized theory of gravity (same as Spin-2 theory in flat spacetime) presentation as linearized limit of general relativity field equations      437—438 461f
Linearized theory of gravity (same as Spin-2 theory in flat spacetime) presentation as linearized limit of general relativity formula for metric      438
Linearized theory of gravity (same as Spin-2 theory in flat spacetime) presentation as linearized limit of general relativity gauge invariance of Riemann curvature      438
Linearized theory of gravity (same as Spin-2 theory in flat spacetime) presentation as linearized limit of general relativity gauge transformations      438 441
Linearized theory of gravity (same as Spin-2 theory in flat spacetime) presentation as linearized limit of general relativity global Lorenu transformations      4.V1
Linearized theory of gravity (same as Spin-2 theory in flat spacetime) presentation as linearized limit of general relativity Lorentz gauge      438 441

Linearized theory of gravity (same as Spin-2 theory in flat spacetime) presentation as linearized limit of general relativity sketched      435
Linearized theory of gravity (same as Spin-2 theory in flat spacetime) presentation from spin-2 viewpoint      179—186
Linearized theory of gravity (same as Spin-2 theory in flat spacetime) self-inconsisiency of      180 443f
Linearized theory of gravity (same as Spin-2 theory in flat spacetime) self-inconsisiency of complete repair of leads to general relativity      186 424f
Lines of force diagram for gravitational waves      101
Lines of force never end, as core of Maxwell’s equations      420
Lines of force relation to honeycomb structure      102
Lorentz force law compared equation of geodesic deviation      35
Lorentz force law derived from Einstein’s field equations      473—475
Lorentz force law double role: defines fields and predicts motions      71—74
Lorentz force law energy change associated with      73
Lorentz force law for a continuous medium      570
Lorentz force law formulated, in flat spacetime      73
Lorentz force law in curved spacetime      201 568
Lorentz force law in language of energy-momentum conservation      155
Lorentz force law in language of forms      101—104
Lorentz force law in three languages      474
Lorentz frame, local closest to global Lorentz frame      207
Lorentz frame, local evidences for acceleration relative to      327
Lorentz frame, local mathematical representations of      217f 285ff 314f
Lorentz frame, local straight lines are geodesies of curved spacetime      312—324
Lorentz frame, local used to analyze redshift experiments      1056—1060 (see also “Inertial frame local”)
Lorentz gauge      see “Gauge transformations and invariance”
Lorentz geometry, global      19—23
Lorentz geometry, global contrasted with Euclidean geometry      51
Lorentz geometry, global spacetime possesses, if and only if Riemann vanishes      284
Lorentz group      242
Lorentz invariance, experimental tests of      1054f
Lorentz transformations      66—69
Lorentz transformations boost      67 69
Lorentz transformations in spin-matrix language      1142—1145
Lorentz transformations in spin-matrix language velocity parameter      1145
Lorentz transformations infinitesimal antisymmetric matrix for      171
Lorentz transformations infinitesimal generator of      329
Lorentz transformations infinitesimal special case: boost along coordinate axis      80
Lorentz transformations key points      67f
Lorentz transformations matrix description of      66
Lorentz transformations post-Newtonian limit of      1086
Lorentz transformations rotation in a coordinate plane      67
Lorentz transformations used to annul Poynting flux      122 (see also “Rotations”)
Lorentz transformations velocity parameter in      67
Lorentz transformations way to remember index positions      66
Lowering indices      see “Index manipulations”
Lunar orbit, experimental tests of general relativity using      1048 1116 1119 1127—1131
Machine with slots      see under “Covariant derivative” “Metric” “Tensor”
Mach’s principle      490 543—545
Mach’s principle acceleration relative to distant stars      543
Mach’s principle and dragging of inertial frames      547 (see also “Dragging of inertial frames”)
Mach’s principle and Foucault pendulum      547
Mach’s principle and York’s formulation of initial-value problem      546
Mach’s principle dragging analoaous to magnetic effect      548
Mach’s principle dragging analoaous to magnetic effect inertial influence of distant stars      548
Mach’s principle dragging analoaous to magnetic effect sum-for-inertia in      549
Mach’s principle dragging analoaous to magnetic effect “flat” space as part of closed space in      549
Mach’s principle gives inertia here in terms of mass there      546
Magnetic flux, from integration of Faraday      99—101
Magnetic poles, absence of      80
Magnetostatics, plus covariance, gives magnetodynamics      80 106
Magnitude-redshift relation      see under “Cosmology observational
Manifold, diflerentiable      10 13 241ff
Many-fingered time, and arbitrariness in slice through spacetime      713f 1184
Mass active vs. passive      see “Cavendish gravitational constant”
Mass center of      161
Mass experimental, finite, as difference between two infinities      474—475
Mass hyperboloid      585
Mass inertial vs. gravitational      431 1051
Mass inertial, density of      159f
Mass-energy, density of      see “Stress-energy tensor”
Mass-energy, total, of an isolated, gravitating system ( $\equiv$ “active gravitational mass”) as geometric object residing in asymptotically flat spacetime      453
Mass-energy, total, of an isolated, gravitating system ( $\equiv$ “active gravitational mass”) conservation law for      455 468—471
Mass-energy, total, of an isolated, gravitating system ( $\equiv$ “active gravitational mass”) contribution of gravitational field to      467
Mass-energy, total, of an isolated, gravitating system ( $\equiv$ “active gravitational mass”) contribution of gravitational field to localizable to within a wavelength for gravitational waves      955f 964ff 969f
Mass-energy, total, of an isolated, gravitating system ( $\equiv$ “active gravitational mass”) contribution of gravitational field to not localizable in generic case      466ff
Mass-energy, total, of an isolated, gravitating system ( $\equiv$ “active gravitational mass”) contribution of gravitational field to precisely localizable only for spherical systems      603f 803f
Mass-energy, total, of an isolated, gravitating system ( $\equiv$ “active gravitational mass”) denned by rate metric approaches flatness in extensor      Chap. 19
Mass-energy, total, of an isolated, gravitating system ( $\equiv$ “active gravitational mass”) denned by rate metric approaches flatness in general      453 455
Mass-energy, total, of an isolated, gravitating system ( $\equiv$ “active gravitational mass”) denned by rate metric approaches flatness in linearized theory      448—450
Mass-energy, total, of an isolated, gravitating system ( $\equiv$ “active gravitational mass”) measured via Kepler’s 1-2-3 law      450 457 636ff
Mass-energy, total, of an isolated, gravitating system ( $\equiv$ “active gravitational mass”) no meaning of for closed universe      457—459
Matrix, inverse, explicit expression for      161 (see also “Jacobian” “Determinant”)
Matter in universe, luminous, mean density of      710f 761
Maxima, number of      318
Maximal analytic extension of a geometry      882
Maxwell energy density      140—141
Maxwell, dual 2-form representation of electromagnetic field, introduced      105 (see under “Electromagnetic field”)
Maxwell’s equations and conservation of energy-momentum      483
Maxwell’s equations component version in flat spacetime      80f
Maxwell’s equations deduced from “lines of force end only on charge”      79—81
Maxwell’s equations derived from physics on a spacelike slice      419—420
Maxwell’s equations derived from stress-energy and Einstein field equation      471—473
Maxwell’s equations for vector potential      569
Maxwell’s equations geometric version      88—89
Maxwell’s equations in curved spacetime      391 568
Maxwell’s equations in language of forms      112—114
Maxwell’s equations nowhere failing      1200 (see also “Electrodynamics” “Lorentz
Maxwell’s equations solution for particle in an arbitrary state of motion      121—122
Mean eccentric anomaly      648
Measurability of geometry and fields in classical theory      13
Measurement, possibilities defined by theory      1184
Measuring rods      see “Rods”
Mercury, perihelion precession of      see “Perihelion shift”
Meshing of local Lorentz frames      190—191
Metric coefficients in specific manifolds and frames      see specific manifolds e.g. “Sphere or e.g. “Kerr
Metric compatibility with covariant derivative      313ff 353f
Metric components of in arbitrary basis      201 310f
Metric components of in Euclidean coordinates      22
Metric components of in Lorentz coordinates      22 53
Metric computation of connection coefficients from      210 216
Metric descriptions as line element      77 305 310
Metric descriptions as machine with slots      22 51—53 77 305 310f
Metric descriptions in component language      77 310f
Metric descriptions in terms of basis 1-forms      77 310
Metric descriptions introduced and defined      22
Metric descriptions summarized      77 305 310f
Metric determinant of components defined      202
Metric determinant of components, differentiated, gives contraction of connection coefficients      222
Metric determinant of components, variation of      503
Metric distilled from distances      306—309
Metric elasticity of space      426—428
Metric enters electromagnetism only in concept of duality      105 114
Metric role in Newton — Cartan spacetime      300 302
Metric role in spacetime of general relativity measured by light signals and free particles      324
Metric role in spacetime of general relativity measured by light signals and free particles, as “gravitational field”      399—400
Metric role in spacetime of general relativity measured by light signals and free particles, components not all predicted by geometrodynamic law      409
Metric role in spacetime of general relativity measured by light signals and free particles, test for local Lorentz character      311—312
Metric structure, and symplectic structure      126
Metric theories of gravity      1067ff
Metric theories of gravity experiments to test whether the correct theory is metric      Chap. 38 1067
Metric theories of gravity PPN formalism as approximation to      1069
Microwave radiation      see “Cosmic microwave radiation”
Minima, number of      318
Minkowski geometry      see “Lorentz geometry”
Missing matter, “mystery of”      710 (see also under “Cosmology”)
Mixmaster oscillations damp chaos      769
Mixmaster universe      805—814
Mobius strip      96
Moment of inertia tensor defined      977
Moment of rotation as meaning of Einstein curvature      373—377
Moment of rotation conservation of      378ff 473
Momentum field, electromagnetic      497f 524
Momentum space      583ff 590
Momentum vector      see “Energy-momentum 4-vector”
Momentum, in mechanics, as space rate of change of action      486—487
Moon effect on tides      44
Moon laser ranging to      1048 1130f
Moon orbit of tests of general relativity using      1048 1116 1119 1127—1131
Moon separation from Earth as gravitational-wave detector      1013f 1018
Moon shadow on Earth      24—26
Morse theory      318
Mossbauer effect      63 1056 1057

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