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

Fermat's principle of least time      185 (problem)
Fermi normal coordinates      see “Freeh-tailing frames”
Fermi pressure      255 151 516—520
fermions      516 see
Flat Earth theory      125—126
Flat space, in Newtonian mechanics      31
Flat spacetime      52—60
Flat spacetime, geometry      53
Flat spacetime, light cones      58—60
Flat spacetime, line element      53 56 81
Flat spacetime, line element, conventions      56n
Flat spacetime, line element, invariance under Lorentz transformations      66
Flat spacetime, metric      81
Flat spacetime, straight timelike lines are longest distances      65
Fluid      see “Perfect fluid”
Force density      478
Foucault pendulum      35 (box) 37
Four-acceleration      see “Special relativistic mechanics”
Four-momentum      see “Special relativisitic mechanics”
Four-vectors      77—85 see
Four-vectors, addition      77
Four-vectors, basis vectors for      78
Four-vectors, defined      77
Four-vectors, displacement      79
Four-vectors, handwritten notation for      79n
Four-vectors, invariance      77
Four-vectors, length      78
Four-vectors, lightlike      see “Null”
Four-vectors, Lorentz transformation      80
Four-vectors, multiplication by numbers      77
Four-vectors, null      78
Four-vectors, scalar product      80—82
Four-vectors, scalar product, defined      81
Four-vectors, scalar product, explicit forms      81
Four-vectors, spacelike      78
Four-vectors, timelike      78
Four-vectors, transformation between inertial frames      80
Four-velocity      see “Special relativistic mechanics”
Four-volume      146—148
frames      see also “Inertial frames” “Local “Freely
Frames, defined      31
frames, rotating      35 (box) 183
Frames, usage discussed      31n
Free indices      see “Indices”
Free particle, in general relativity      169
Free particle, in Newtonian mechanics      31
Free particle, notions in general relatyvity and Newtonian mechanics compared      169n
Freely falling frames      181—183 440—441
Freely falling frames, and drag free satellites      182 (box)
Freely falling frames, construction      182 308
Freely falling frames, in the Schwarzschild geometry      441
Freely falling frames, other terms for      182n
Freely falling frames, propagation of basis vectors      440
Friedman equation      see “FRW cosmological models”
Friedman — Robertson — Walker cosmological models      see “FRW cosmological models”
FRW cosmological models      366—413 see
FRW cosmological models, $\Omega$ defined      389
FRW cosmological models, ${\Omega}_{baryon}$       400 401
FRW cosmological models, ${\Omega}_{c}$       391
FRW cosmological models, ${\Omega}_{m} {\Omega}_{v} {\Omega}_{r}$       377
FRW cosmological models, age      381 392
FRW cosmological models, big bang      379 380
FRW cosmological models, big bang, as a singularity      380
FRW cosmological models, closed models      385
FRW cosmological models, closed models, finite volume but no boundary      385
FRW cosmological models, closed models, line element      387
FRW cosmological models, closed models, qualitative evolution      393
FRW cosmological models, comoving coordinates      367
FRW cosmological models, cosmological fluid      367 372
FRW cosmological models, critical density      377 389
FRW cosmological models, defining approximations      366 372
FRW cosmological models, dimensionless variables for      391
FRW cosmological models, effective potential      378 (figure) 391 394
FRW cosmological models, Einstein equation for      484
FRW cosmological models, Einstein static universe      398 (problem)
FRW cosmological models, evolution of curved models      387—395
FRW cosmological models, evolution of curved models, big crunch      390
FRW cosmological models, evolution of curved models, explicit solution for matter dominated models      389
FRW cosmological models, evolution of curved models, Mathematica program for computing      see “Website”
FRW cosmological models, evolution of curved models, qualitative behavior      393—395
FRW cosmological models, evolution of flat models      376—380
FRW cosmological models, evolution of flat models, explicit solutions for matter, radiation, and vacuum dominated cases      378
FRW cosmological models, evolution of flat models, normalization of scale factor      377
FRW cosmological models, evolution of flat models, three stages      378 (figure) 379
FRW cosmological models, expansion      367
FRW cosmological models, expansion, what's expanding? into what? from where?      367
FRW cosmological models, first few minutes      380
FRW cosmological models, flat models      366—368
FRW cosmological models, flat models, evolution      378
FRW cosmological models, flat models, line element      366
FRW cosmological models, Friedman equation      387 388 484
FRW cosmological models, Friedman equation, Mathematica program for solving      see “Website”
FRW cosmological models, Friedman equation, motivated by Newtonian physics for pressureless matter      388
FRW cosmological models, Friedman equation, rescaled form      391
FRW cosmological models, geometries of space      384—386
FRW cosmological models, geometries of space, closed      385
FRW cosmological models, geometries of space, curvature of      386
FRW cosmological models, geometries of space, embedding diagrams      386 (figure)
FRW cosmological models, geometries of space, flat models      367
FRW cosmological models, geometries of space, open      385
FRW cosmological models, homogeneous, isotropic spacetimes      366—368 384—387
FRW cosmological models, homogeneous, Robertson — Walker metrics      367 368 384 387
FRW cosmological models, horizon      382 383 407
FRW cosmological models, horizon, growth during inflation      412
FRW cosmological models, horizon, matter and radiation dominated flat models      383
FRW cosmological models, horizon, present size      383
FRW cosmological models, horizon, size of region in causal contact      407
FRW cosmological models, Hubble constant      371
FRW cosmological models, Hubble'slaw      371
FRW cosmological models, inflation      412
FRW cosmological models, k parameter      387
FRW cosmological models, last-scattering surface      407 (figure)
FRW cosmological models, light cones      383 (figure)
FRW cosmological models, line elements summarized      387
FRW cosmological models, local conservation of stress-energy      481
FRW cosmological models, luminosity distance      403n
FRW cosmological models, Mathematica program for evolution      see “Website”
FRW cosmological models, matter      373
FRW cosmological models, matter dominated models      389
FRW cosmological models, matter dominated models, explicit solutions      390
FRW cosmological models, matter, energy density ${\rho}_{m}$       373
FRW cosmological models, matter, pressure ${\rho}_{m} = 0$       373
FRW cosmological models, matter, variation with scale factor      373
FRW cosmological models, metrics summarized      387
FRW cosmological models, open models      386
FRW cosmological models, open models, line element      387
FRW cosmological models, open models, qualitative evolution      393
FRW cosmological models, parameters ${H}_{0}, {\Omega}_{r}, {\Omega}_{m}, {\Omega}_{v}$       392 400 see cosmological
FRW cosmological models, parameters ${\Omega}_{m}-{\Omega}_{v}$       395 (figure)
FRW cosmological models, particle horizons      see “Horizon”
FRW cosmological models, radiation      373—374
FRW cosmological models, radiation, energy density ${\rho}_{r}$       374
FRW cosmological models, radiation, energy density today      400
FRW cosmological models, radiation, pressure ${p}_{r} = {\rho}_{r}/3$       373
FRW cosmological models, radiation, temperature T      373
FRW cosmological models, radiation, variation with scale factor      374
FRW cosmological models, redshift      368—372
FRW cosmological models, redshift-(angular size) relation      407—408 414
FRW cosmological models, redshift-magnitude relation      402—405 414
FRW cosmological models, redshift-number relation      414 (problem)
FRW cosmological models, scale factor      366 372
FRW cosmological models, singularity theorem      399 (problem)
FRW cosmological models, thermodynamics, first law of      372—373
FRW cosmological models, vacuum, cosmological constant      376
FRW cosmological models, vacuum, energy density ${\rho}_{v}$       374
FRW cosmological models, vacuum, pressure ${p}_{v} = {-\rho}_{v}$       376
Functional      43
Future light cones      see “Light cones”
Galaxies, as components of the universe      349 (figure)
Galaxies, smoothed out energy density      348

Galaxies, typical properties      347
Galilean transformation      36 47 49
Gamma-ray bursts      510
Gauge transformations in electromagnetism      462 (table)
Gauge transformations in linearized gravity      see “Linearized gravity”
Gauss, C.F., test of plane geometry      15
General relativity      3—537
General relativity, compared to Newtonian gravity      452 (table) 486
General relativity, compared to Newtonian gravity formulated geometrically      129 (table)
General relativity, gravitomagnetic effects      303
General relativity, tests of      see “Gravitational redshift” “Deflection “Precession “Time “Binary “Gyroscopes”
Geodesic deviation, equation of      450—454
Geodesic deviation, equation of, compared with Newtonian deviation equation      452 (table)
Geodesic deviation, equation of, in freely falling frame      452
Geodesic deviation, equation of, Newtonian limit      453—154
Geodesic equation      169—174
Geodesic equation, compared with Newton's second law      452 (table)
Geodesic equation, conservation laws      176—178
Geodesic equation, conserved normalization of u      176
Geodesic equation, equations vs. equation      173n
Geodesic equation, expressed with covanant demames      434
Geodesic equation, first integrals      176 178 see
Geodesic equation, for plane in polar coordinates      171
Geodesic equation, for wormhole geometry      172
Geodesic equation, general form      173
Geodesic equation, in terms of four-velocity      173
Geodesic equation, Lagrangian for      172
Geodesic equation, procedure for finding      171 Mathematica see
Geodesic equation, table comparing in flat, Newtonian, and general spacetimes      170 (table)
Geodesic equation, tor null geodesic      179
Geodesies      see also “Geodesic equation”
Geodesies, as paths of extremal proper time      170
Geodesies, defined      170
Geodesies, null      178—179
Geodesies, null, geodesic equation      179
Geodetic precession      see “Gyroscopes”
Geometized units      see “Units”
Geometry, defined by distance between nearby points      21
Geometry, differential      21
Geometry, intrinsic description      20
Geometry, line element specifies      23
Geometry, measurement of      15—17
Geometry, same geometry described in different coordinates      135
Geometry, ways of describing      20—21
Global Positioning System (GPS)      3 121—125
Global Positioning System (GPS), rate difference between signal emission and reception      124
Global Positioning System (GPS), simultaneity in      69 125
Global Positioning System (GPS), time dilation in      124
Global Positioning System (GPS), toy model      69
GP-B experiment      182 (box) 305
GPS      see “Global Positioning System“”
Gradient (three-dimensional), and covariant Jemative      437 (box)
Gradient (three-dimensional), formula tor in flat three-space      437 (box)
Gradient, and normal vectors      426
Gradient, as a covariant derivative      435
Gradient, as a dual vector      421
Gradient, defined      421
Graviational collapse, general      8 275—276 310—311 see
Graviational collapse, general cosmic censorship ton eaure      275
Graviational collapse, general formation of a Mat k hole      275 281
Graviational collapse, general formation of a singularity      275
Graviational collapse, general singularity theorems      275
Graviational collapse, general, big crunch      390
Gravitational binding, energy released in      290 (box)
Gravitational binding, vs. thermonuclear fusion      290 (box)
Gravitational collapse, spherical      262—268
Gravitational collapse, spherical, area of horizon increases      268 278
Gravitational collapse, spherical, formation of a black hole      264 (figure) 265—268
Gravitational collapse, spherical, inside the horizon      262—265
Gravitational collapse, spherical, inside the horizon, no escape after horizon crowed      265
Gravitational collapse, spherical, inside the horizon, singularity hidden inside horizon      265
Gravitational collapse, spherical, inside the horizon, singularity inevitable after horizon crosed      265
Gravitational collapse, spherical, of dust      262
Gravitational collapse, spherical, outside the horizon      265—268
Gravitational collapse, spherical, outside the horizon, indistinguishable from Schwarz^hild geometry      267
Gravitational collapse, spherical, outside the horizon, lumminocity approaches zero      267
Gravitational collapse, spherical, outside the horizon, never crosses       265
Gravitational collapse, spherical, outside the horizon, redshift approaches intinity      265 266
Gravitational collapse, spherical, outside the horizon, time seaeditor approaching a black hove      267
Gravitational collapse, spherical, story observers      264—268 272 274
Gravitational constant G.      38
Gravitational held      see “Newtonian gravity”
Gravitational ineraction      see also “Relitivitic gravity”
Gravitational ineraction, governuniverse on largescales      4
Gravitational ineraction, long range      4 516
Gravitational ineraction, Newton's law      3
Gravitational ineraction, strength ot compared to ether forces      4
Gravitational ineraction, universal      4
Gravitational ineraction, unscreened      4
Gravitational ineraction, where important      4
Gravitational lensing      234—243
Gravitational lensing, achromatic      238
Gravitational lensing, by MACHOs      242—243
Gravitational lensing, by MACHOs, characteristic variation time      243
Gravitational lensing, Einstein angle      237
Gravitational lensing, Einstein ring      237
Gravitational lensing, idea      235 (figure)
Gravitational lensing, images, brightness      240—243
Gravitational lensing, images, number      238 253
Gravitational lensing, images, positions      238
Gravitational lensing, images, shapes      238 (figuie 1
Gravitational lensing, lens equation      236 (figure) 237
Gravitational lensing, macrolensing      237
Gravitational lensing, microlensing      237 243
Gravitational lensing, surface brightness      240
Gravitational lensing, thin lens approximation      236
Gravitational lensing, time difference between fluctuations in images      242
Gravitational lensing, used to measure mass      239
Gravitational lensing, uses      234
Gravitational mass      41—42 108—109
Gravitational mass, and weight      42
Gravitational mass, defined      41
Gravitational mass, equality with inertial mass      42
Gravitational physics      3—12
Gravitational physics, two frontiers      3
Gravitational potential      see “Newtonian gravity”
Gravitational radiation      see “Gravitational waves”
Gravitational redshift      119
Gravitational redshift, measured in spectra      219
Gravitational redshift, Schwarzschild geometry      189—191
Gravitational redshift, tests      118 (box) 219—221
Gravitational waves      9 331—344 459—466 491—511 also
Gravitational waves, analogies with electromagnetism      501 (table) 501—502 507
Gravitational waves, angular momentum loss      512 (problem)
Gravitational waves, astrophysical interest      331
Gravitational waves, detection      9 331 333—342 491
Gravitational waves, detection, interferometers      339—342
Gravitational waves, detection, LIGO      341
Gravitational waves, detection, Michelson interferometer      339 (figure)
Gravitational waves, detection, single test mass not enough      333
Gravitational waves, effect of detected in binary pulsar      508—509
Gravitational waves, energy density      342—344
Gravitational waves, energy flux      332 343
Gravitational waves, ertect on test masses      332—336 337
Gravitational waves, from binary stars      502—509 see also “Binary pulsar”
Gravitational waves, from binary stars, amplitude far away      504
Gravitational waves, from binary stars, angular power distribution      505—506
Gravitational waves, from binary stars, decrease in period      508
Gravitational waves, from binary stars, estimates for i Boo      500
Gravitational waves, from binary stars, frequency twice orbital frequency      504
Gravitational waves, from binary stars, long wavelength approximation satisfied      503
Gravitational waves, from binary stars, polarization      505—5116
Gravitational waves, from merging black holes      510
Gravitational waves, large r approximation      498—502
Gravitational waves, linearized      331 333
Gravitational waves, linearized, amplitude      332
Gravitational waves, linearized, metric and metric perturbations      332 492
Gravitational waves, linearized, superposition of      333
Gravitational waves, long wavelength (slow motion) approximation      498—502
Gravitational waves, metric perturbations at large r      499

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