Hartle J.B. — Gravity: An Introduction to Einstein's General Relativity :: Электронная библиотека попечительского совета мехмата МГУ

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Hartle J.B. — Gravity: An Introduction to Einstein's General Relativity

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Название: Gravity: An Introduction to Einstein's General Relativity

Автор: Hartle J.B.

Аннотация:

A textbook for junior or senior undergraduate physics students. It begins with the simplest physically relevant solutions of the Einstein equation to bring students quickly to the physical phenomena.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2002

Количество страниц: 656

Добавлена в каталог: 14.04.2008

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Предметный указатель

Gravitational waves, no monopole or dipole      502 511
Gravitational waves, plane      332
Gravitational waves, polarization      332 336—338
Gravitational waves, polarization + and x polarizations      338 465
Gravitational waves, polarization circular      345 (problem)
Gravitational waves, production of      498—500
Gravitational waves, quadrupole formula for energy loss      506—508
Gravitational waves, quadrupole formula, limitations of      510
Gravitational waves, solutions to the linearized Einstein equation      464—466
Gravitational waves, sources      331 491 see “Merging etc.
Gravitational waves, sources, strong      491 510—511
Gravitational waves, speed      332
Gravitational waves, strain produced by      336
Gravitational waves, transverse      332 336
Gravitomagnetic effects      296 303
Gravitons      91
Gravity is geometry      4 13—15 125—131
Gravity Probe B.      see “GP-B experiment”
Ground state matter      524—528
Ground state matter, equation of state      526 (box) 527
Ground state matter, mass vs. radius for      528 (figure)
Ground state matter, neutron drip      526 (box)
Ground state matter, neutron matter      526 (box)
Gyro      see “Gyroscopes”
Gyroscopes      35 (box) 297—308
Gyroscopes, and the dragging of inertial frames      see “Lense — Thirring precession”
Gyroscopes, equation of motion for spin formulated With covariant derivative      438
Gyroscopes, equation of motion for spin in a local menial frame      298
Gyroscopes, equation of motion for spin in curved spacetime      298
Gyroscopes, geodetic precession      298—302
Gyroscopes, geodetic precession, measured by GP-B      305 (box)
Gyroscopes, in curved spacetime      297—298
Gyroscopes, in the spacetime of slowly-rotating body      303—307
Gyroscopes, Lense — Thirring precession      306—308
Gyroscopes, Lense — Thirring precession, measured by GP-B      305 (box)
Gyroscopes, spin four-vector      297
Gyroscopes, thought experiment for measuring dragging of inertial frames      303—307
GZK cutoff for cosmic rays      95 (box)
GZK effect      94 (box)
GZK effect, limits rotation of the universe      37 (box)
GZK effect, spectrum      350 (figure)
GZK effect, temperature      350 (figure) 361
Hawking radiation      see “Black holes”
Hawking, S.      289
Hertzsprung — Russell diagram      357 (figure)
Hipparcos satellite      354 357
Homogeneous, isotropic cosmological models      see “FRW cosmological models”
Horizon, cosmological      see “FRW cosmological models”
Horizon, event horizon      see “Black holes”
Horizon, of a black hole      see “Black holes”
Hubble constant, defined      352
Hubble constant, relation to the scale factor      371
Hubble constant, value      352 360
Hubble Deep Field      349 (figure)
Hubble diagram      360 (figure)
Hubble distance ${d}_{H}$       382
Hubble parameter h      372
Hubble Space Telescope      96
Hubble time ${t}_{H}$       361 371
Hubble's Law      352—359 360
Hubble's law, and homogeneity      353
Hubble's law, for FRW models      371
Hubble's law, stated      352
Hulse — Taylor binary pulsar      see “Binary pulsar PSRB1913+16”
Hulse, R., and discovery of the binary pulsar PSRB1913+16      250
Hydrostatic equilibrium      see “Relativistic stars equations
Hyperbolic angles      58
Hyperbolic plane      184 (problem)
Hypersurface      see “Three-surfaces”
Indices, balancing      139
Indices, contravariant      423
Indices, covariant      423
Indices, downstairs      see “Covariant”
Indices, dummy      see “Summation”
Indices, free      80 139
Indices, names for (upper and lower, upstairs and downstairs, contravariant and covariant)      423n
Indices, raising and lowering in coordinate bases      422 423
Indices, raising and lowering in orthonormal bases      423
Indices, raising and lowering on tensors      427
Indices, raising and lowering on the metric tensor      427
Indices, summation      79 139
Indices, upstairs      see “Contravariant”
Inertial frames      see also “Local inertial frames”
Inertial frames, and free particle motion      32
Inertial frames, and twin paradox      65
Inertial frames, connected by Lorentz transformations      65
Inertial frames, connection between      34—36 49
Inertial frames, construction of      32 52
Inertial frames, defined      32
Inertial frames, defined by free particles and gyroscopes      32
Inertial frames, defined by Newton's first law      34
Inertial frames, in Newtonian mechanics      31—36
Inertial frames, not all frames are inertial      34
Inertial frames, rotational dragging      296—297
Inertial frames, rotational dragging, measured by GP-B      305 (box)
Inertial mass      41—42 107—109
Inertial mass, defined      41
Inertial mass, equality with gravitational mass      42
Infinity, different kinds of: future and past null $({J}_{\pm})$ , future and past timelike $({I}_{\pm})$ , spacelike $({J}_{0})$       137 (box) 274
Inflation      see “Universe” “FRW
Interference pattern      340 (figure) 345
Inverse metric      see “Metric”
Inverse square law      354
Inverse square law, in cosmology      402
Iron peak nuclei, ashes of thermonuclear burning      255
ISCO, innermost stable circular orbit      see “Schwarzschild geometry” “Kerr
Kepler's law      see “Newtonian gravity”
Kerr black holes      296 310—328 see
Kerr black holes, a, maximum realistic salue      313
Kerr black holes, accretion disk around      313
Kerr black holes, and active galactic nuclei      326—327(box)
Kerr black holes, angular velocity      314 315
Kerr black holes, Blandford — Znajek mechanism      326—327 (box)
Kerr black holes, extreme      313
Kerr black holes, Hawking temperature      330 (problem)
Kerr black holes, horizon      313—316
Kerr black holes, rotational energy      325 326—327
Kerr geometry      310—328 also “Black
Kerr geometry, ${r}_{\pm}$ not singular      313
Kerr geometry, angular momentum      311
Kerr geometry, angular momentum, defined by distant gyro      312
Kerr geometry, angular momentum, maximum realistic value      313
Kerr geometry, angular momentum, maximum value      313
Kerr geometry, as a black hole      313—316
Kerr geometry, asymptotically flat      312
Kerr geometry, Boyer — Lindquist coordinates, coordinate singularity      312
Kerr geometry, Boyer — Lindquist coordinates, metric      311
Kerr geometry, ergosphere      322—328
Kerr geometry, ergosphere, no stationary observers inside      322
Kerr geometry, extracting rotational energy      323—328
Kerr geometry, extracting rotational energy, Penrose process      323—328
Kerr geometry, extreme      313
Kerr geometry, horizon      313—316
Kerr geometry, horizon, angular velocih      314—315
Kerr geometry, horizon, area      316
Kerr geometry, horizon, as a null three-surface      314—316
Kerr geometry, horizon, embedding diagram      316 (figure)
Kerr geometry, horizon, geometry      315 316
Kerr geometry, horizon, location      314
Kerr geometry, horizon, null generators      314—315
Kerr geometry, horizon, one way property      316
Kerr geometry, irreducible mass      325
Kerr geometry, irreducible mass, and area increase      325
Kerr geometry, Kerr parameter a      311
Kerr geometry, Killing vectors      312
Kerr geometry, mass      311
Kerr geometry, mass measurable by distant test particle orbit      312
Kerr geometry, not a black hole for a > M      319
Kerr geometry, orbits in the equatorial plane      316—321
Kerr geometry, orbits in the equatorial plane, conserved angular momentum      317

Kerr geometry, orbits in the equatorial plane, conserved energy      317
Kerr geometry, orbits in the equatorial plane, effective potentials      318
Kerr geometry, orbits in the equatorial plane, ISCO (innermost stable circular particle orbit)      320—321
Kerr geometry, orbits in the equatorial plane, ISCO binding energy      321 (figure)
Kerr geometry, orbits in the equatorial plane, ISCO radius      320 (figure)
Kerr geometry, orbits in the equatorial plane, radial plunge      318
Kerr geometry, Penrose process      323—328
Kerr geometry, rotational energy      325
Kerr geometry, Schwarzschild when not rotating      312
Kerr geometry, singularity      312
Kerr geometry, stationary observers      322—323
Kerr geometry, symmetries      312
Kerr geometry, unique black hole solution of the vacuum Einstein equation      310
Kerr geometry, what's rotating?      315
Kerr metric      see “Kerr geometry”
Kerr, R.      310
Killing vectors, and conserved quantities      177
Killing vectors, characterize symmetries      176
Killing vectors, defined      176
Killing vectors, Killing's equation      443 (problem)
Killing vectors, of flat space      177
Killing. W      176
Kronecker S      422
Kruskal coordinates, metric, diagram, extension etc.      see “Schwarzchild geometry”
Lagrange's equations      43 44 90
Lagrangian      43
Lagrangian, for free particle motion      90
Large Magellanic Cloud (LMC)      242
LBI      see “Long base-line radio interferometry”
Lem, S.      74 (problem)
Length      146—148
Lens equation, see      “Gravitational lensing”
Lense — Thirnng precession      see “Gyroscopes”
Lensing      see “Gravitational lensing”
LiF      see “Local inertial frames”
Life history of a star      see “Stellar evolution”
Light cones      58—60 142—145
Light cones, and simultaneity      59
Light cones, as null surfaces      162
Light cones, define "before" and "after"      59
Light cones, defined      58
Light cones, dehne causal relationships      59
Light cones, future      59
Light cones, inside      59
Light cones, null cones as an alternative name      58n
Light cones, outside      59
Light cones, past      58 59
Light rays      91—94 also
Light rays, affine parameters for      91 179
Light rays, null world lines of      59 91—92
Light rays, tangent vectors to      91
Lightlike      see “Null”
LIGO (Laser Interferometer Gravitational (Wave) Observatory)      341—342
Line element      see also “Specific geometries for specific forms”
Line element, and metric      138
Line element, defined      23
Linearized Einstein equation      see “Linearized gravity”
Linearized gravity      459—466 491—508
Linearized gravity, analogies with electromagnetism      462 (table)
Linearized gravity, gauge conditions      462
Linearized gravity, gauge transformations      461—163
Linearized gravity, gauge transformations, compared with gauge transformations in electromagnetism      462 (table)
Linearized gravity, general solution      496—198
Linearized gravity, general solution, satisfies Lorentz gauge      496
Linearized gravity, linearized Einstein equation      459—466 491—493
Linearized gravity, linearized Einstein equation, in Lorentz gauge      463 492
Linearized gravity, linearized Einstein equation, plane wave solutions      464—166
Linearized gravity, linearized Einstein equation, vacuum      463 492
Linearized gravity, linearized Ricci cunature      492
Linearized gravity, Lorentz gauge      463 492
Linearized gravity, metric perturbations      459 492
Linearized gravity, metric perturbations, raising and lowering indices      460
Linearized gravity, slow rotation, solution tor      497—498
Linearized gravity, transverse-traceless (TT) gauge      465
Linearized gravity, transverse-traceless (TT) gauge, transforming to      466
Linearized gravity, weak sources, low velouties assumed      492
LISA gravitational wave detector      10 (figure)
LMC      see “Large Magellanic cloud”
Local inertial frames      140—142 179—183
Local inertial frames, construction of      180
Local inertial frames, Riemann normal coordinates an example      180
Local inertial frames, transforming to      165 (problem)
Long base-line radio interferometry (LBI)      225
Lorentz boosts      65—68
Lorentz boosts, and simultaneity      68
Lorentz boosts, explicit form      67
Lorentz boosts, special case of Lorentz transformations      67n
Lorentz contraction      70
Lorentz frames      see “Inertial frames”
Lorentz gauge      see “Linearized gravity”
Lorentz hyperboloid      160
Lorentz transformations      see also “Lorentz boosts”
Lorentz transformations, connect inertial frames      65
Lorentz transformations, defined      66
Lorentz transformations, preserve the line element of flat spacetime      66
Lunar laser ranging      14 (box)
Lunenberg lens      185 (problem)
Mach's principle      37 (box)
Mach, E.      37 (box)
MACHOs (Massive compact halo objects)      242—243
Macrolensing      see “Gravitational lensing”
Magnitude, absolute      356
Magnitude, apparent      356
Magnitude, distance modulus      356
Magnitude-redshift relation      see “FRW redshift-magnitude relation”
Main sequence      356 357
map projections      25—26 (box)
Map projections, equal area      29 (problem)
Map projections, equirectangular      25 (box)
Map projections, Mercator      25 (box)
Mass density $\mu(x)$ in Newtonian gravity      39
Mass function      see “Binary stars”
Mass measured by gravitational lensing      239
Mass measured/defined by distant orbit      187
Mass moment tensors, moment of inertia tensor      499n
Mass moment tensors, quadrupole      507
Mass moment tensors, second      499
Massive Compact Halo Objects      see “MACHOs”
Matter in its ground state      see “Ground state matter”
Maximum mass of white dwarfs and neutron stars      256 283 358
Maximum mass of white dwarfs and neutron stars, bound on      535—537 539
Maximum mass of white dwarfs and neutron stars, Chandrasekhar mass      524 525
Maxwell's equations      47 419 445 483
Maxwell's equations, and inertial frames      48
Maxwell's equations, imply speed of light c      47
MCG-6-30-15      249
Mdssbauer effect      118 (box)
Mechanics, Newtonian      see “Newtonian mechanics”
Messier catalog      285n
Metric perturbations      see “Linearized gravity”
Metric, and line element      138
Metric, as a tensor      427
Metric, coordinate transformation of      138 164
Metric, covariant derivative vanishes      438
Metric, defined      138
Metric, in a local inertial frame      140
Metric, inverse      422
Metric, number of independent functions      138
Michelson interferometer      339—341
Michelson — Morley experiment      47—49 see
Microlensing      see “Gravitational lensing”
Milky Way (our galaxy)      287 (figure)
Minkowski space      see “Flat spacetime”
Minkowski, H.      56
Momentum, as a component of stress-energy      474
Momentum, conservation of in flat spacetime      478^79
Momentum, density      474—477
Momentum, density equals energy flux      475
Momentum, local conservation of in curved spacetime      480—482
Muon lifetime and time dilation      64 (box)

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