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









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: Gravity: An Introduction to Einstein's General Relativity

: Hartle J.B.

:

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.


: en

: /

:

ed2k: ed2k stats

: 1st edition

: 2002

: 656

: 14.04.2008

: | | ID
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$^{56}{Fe}$, most bound nucleus made in stars      255
(Angular size)-redshift relation      see FRW cosmological models redshift-(angular
.d'Alembertian      see Wave operator
.i Boo binary star system      346 (problem) 500
2dF redshift survey      364 (figure)
Absolute magnitude      see Magnitude
Acceleration in curved spacetime      434
Acceleration in flat spacetime      86
Accretion disks      244250
Accretion disks, and X-ray sources      244 282
Accretion disks, Eddington limiting luminosity      245 (box)
Accretion disks, formation      244
Accretion disks, radiation from      244
Accretion disks, spectral lines      246250
Accretion disks, spectral lines, Fe line in MCG-6-30-15      249
Accretion disks, spectral lines, frequency shift      248
Accretion disks, temperature estimate      245 (box)
action      see Newtonian mechanics
Active galactic nuclei      288289
Active galactic nuclei, Blandford Znajek mechanism      326327 (box)
Active galactic nuclei, Cygnus A      289 (figure)
Active galactic nuclei, luminosity      288
Active galactic nuclei, powered by black holes      288289 326327
Active galactic nuclei, radio jets      288
Active galactic nuclei, size      288
Active galactic nuclei, spectrum      288
Addition of velocities, Newtonian      47
Addition of velocities, special relativity      71
Affine parameters      see Light rays
AGN      see Active galactic nuclei
Alternating tensor (three dimensions)      438 (box)
And cosmic ray energies      94 (box)
Andromeda galaxy (M31)      348 (figure) 351
Angular momentum, measured/defined by orbiting gyroscope      307
APM galaxy survey      363 (figure)
Apparent magnitude      see Magnitude
Area      146148
Area increase theorem      see Black holes
Arecibo radio telescope      250 (figure) 509
ASCA X-ray satellite      249
Atom interferometry      35 (box)
Baryosynthesis      see Universe thermal
Bases      78 152158 424427
Bases, basis vectors      78
Bases, coordinate      155 420
Bases, dual to a given basis      424427
Bases, orthonormal      153158
Bases, orthonormal, construction along orthogonal coordinate directions      156
Bases, orthonormal, hats on the indices ot      96
Bases, orthonormal, of an observer      97 154
Bases, parallel propagation      440
Bases, table summarizing relations between bases and dual bases      425 (table)
Bases, transforming between coordinate and orthonormal bases      156 429
Bases, transforming between coordinate bases      429430
Beaming      see Relativistic beaming
Bekenstein Hawking formula for black hole entropy      294
Berkeley, G.      37 (box)
Bianchi identity      457 482 489
big bang      3 10 12 see
Big crunch      see FRW cosmological models evolution
Binary pulsar PSR B1913-16, effect on orbital period detected      509 (figure)
Binary pulsar PSR B1913-16, gravitational waves from, effect on orbital period calculated      508
Binary pulsar PSR B1913-16, masses of components determined by general relativity      253
Binary pulsar PSR B1913-16, parameters determined by Newtonian gravity      252
Binary pulsar PSR B1913-16, precession of the periastron      251
Binary pulsar PSR B1913-16, relativistic effects measured      252
Binary pulsar PSR B1913-16, rotational period      252
Binary pulsar PSR B1913-16, semi-major axis      254 (problem)
Binary pulsar PSR B191316      250
Binary pulsars      250 see pulsar
Binary stars, gravitational radiation from      see Gravitational waves
Binary stars, mass function      252 284
Binary stars, radial velocity curve      252 283
Birkhoffs theorem      459 468
Black holes      79 244 256276 310328 also Kerr
Black holes, accretion disks around      282
Black holes, and active galactic nuclei      288 289 326327
Black holes, and cosmic censors      275
Black holes, area increase theorem      276 325
Black holes, defined      261
Black holes, Hawking radiation      289294
Black holes, horizon      8 261 313314
Black holes, how detected      268 283
Black holes, in X-ray bmanes      281285
Black holes, Kerr geometries as the unique family of black holes      276 310
Black holes, nonspherical collapse to      275276
Black holes, primordial      281
Black holes, primordial, exploding      281
Black holes, quantum evaporation      289294
Black holes, rocket thrust required to escape      261 (box)
Black holes, rotating      see Kerr black holes Kerr
Black holes, spherical collapse to      262268
Black holes, supermassive      see Black hoW in galaxy centers
Black holes, surface gravity      443 (problem)
Black holes, thermodynamics      294
Black holes, thermodynamics, first law of      294
Black holes, thermodynamics, second law ot      294
Black holes, thermodynamics, temperature      242
Blandford Znaiek mexhanism      see Kerr black noes
Boomerang experimen      see Cosmic backgroung radiation
Boomerang experiment      18 (box)
Charge, charge-current four-vector      473
Charge, conservation of      473
Charge, current      473
Charge, density      473
Christoffel symbols, defined      173
Christoffel symbols, formula for      174
Christoffel symbols, Mathematica notebook for calculating      see Website
Clocks, devices to measure timelike distances      60
Clocks, in a gravitational field      113121 124
Clocks, in GPS      121
CMB      see Cosmic background radiation
COBE satellite      350 (figure) 361
Conservation      478479 see
Conservation, and spacetime symmetries      176 342 489
Conservation, of a quantity      see That quantity
Conservation, of charge      473
Conservation, of energy-momentum in flat space      478
Conserved quantities along a geodesic      see Geodesic equation
Coordinate bases      see Bases coordinate
Coordinate singularity      136 258
coordinates      135136 also e.g. Schwarzschild Eddington
Coordinates, and gauge transformations in linearized giavity      461
Coordinates, arbitrary but systematic labels of points      2728 135
Coordinates, Cartesian      21
Coordinates, different coordinates describe the same geometry      135
Coordinates, Fermi normal      182n
Coordinates, labels of points      21
Coordinates, latitude and longitude      25 (box)
Coordinates, physics independent or chohse of      27
Coordinates, plane polar      22
Coordinates, Riemann normal      180183
Coordinates, singular      136
Coordinates, spherical polar      136
Coordinates, transformation of      28 136 420 429430
Coordinates, utility of      135
Cosmic background radiation (CMB)      11 348 361 405410
Cosmic background radiation (CMB), angular size      407408
Cosmic background radiation (CMB), anisotropies      358 405410
Cosmic background radiation (CMB), correlation function      408 409
Cosmic background radiation (CMB), signatures of deiiMtv fluctuations that grew to be galaxies      361
Cosmic censorship conjecture      275 310311 (box)
Cosmic rays      94 (box)
Cosmological constant      376 480 483
Cosmological fluid      see FRW cosmological models
Cosmological models      see FRW cosmological models
Cosmological parameters      see FRW cosmological models
Cosmological redshift      351 352 370
Cosmology      see Universe FRW
Covariant derivative      419 430440
Covariant derivative, and parallel propagation      438
Covariant derivative, defined      431
Covariant derivative, formula for ${\nabla}_{\alpha}{v}^{\beta}$      434
Covariant derivative, formula for ${\nabla}_{\alpha}{v}_{\beta}$      436
Covariant derivative, of functions      435
Covariant derivative, of tensors      436
Covariant derivative, of the metric vanishes      438
Covariant derivative, of vectors      see Vectors derivatives
Covectors      see Dual vectors
Crab Nebula      7 (figure)
Critical density      see FRW cosmological models
Curl (three-dimensional), and covariant derivative      438 (box)
Curl (three-dimensional), formula for in flat three-space      438(box)
Currents, fluxes through timelike three-surfaces      473
Curvature      452456
Curvature, Einstein      458
Curvature, Einstein, defined      483
Curvature, Mathematica program for computing      see Website
Curvature, measurement of, by relative test particle motion      445
Curvature, measurement of, two test particles needed      445
Curvature, Ricci      471
Curvature, Ricci scalar, defined      482
Curvature, Ricci, defined      456
Curvature, Ricci, symmetry      456
Curvature, Riemann, defined      452
Curvature, Riemann, dimensions      455
Curvature, Riemann, for static, weak field metric      454
Curvature, Riemann, in a local inertial frame      454
Curvature, Riemann, number of components      454
Curvature, Riemann, of the Schwarzschild geometry      455
Curvature, Riemann, order of magnitude      455
Curvature, Riemann, properties      454455
Curvature, Riemann, symmetries      454
Curvature, scale of      455
Cygnus A radio source      289 (figure)
Dark matter      242 347 349351
Deflection of light      see also Schwarzschild geometry light
Deflection of light, and PPN parameters      223
Deflection of light, confusion with effect of solar corona      226 233
Deflection of light, effect on star field      224 (figure)
Deflection of light, experimental tests      223227
Deflection of light, gravitational lensing      235
Deflection of light, measured in solar eclipses      223 225
Deflection of light, radio observations      224227
Degenerate free fermions      516
Degenerate free fermions, density of states      518
Degenerate free fermions, equation of state      518520
Degenerate free fermions, Fermi momentum      518
densities      471480
Densities, fluxes through spacelike three-surfaces      473
Densities, of a specific quantity      see The quantity
Densities, of scalars, as components of a four-vector      473
Densities, of vectors, as components of a tensor      474
Directional derivatives, correspondence with vectors      420
Directional derivatives, of functions      419
Distance ladder      see Universe distance
Distance modulus      356
Divergence (three-dimensional), and covariant derivative      437 (box)
Divergence (three-dimensional), formula for in flat three-space      437 (box)
Divergence theorem in four dimensions      487 (problem)
Doppler shift      9293
Drag free satellites and freelv tailing frames      182 (box)
Dragging of inertial frames      see Inertial frames
Dual vectors      419 421423 see
Dual vectors, bases for      421
Dual vectors, components      421
Dual vectors, correspondence with vectors      422
Dual vectors, defined      421
Dual vectors, identified with vectors      423
Dummy indices      see Indices
Dust      262 480
Dust, in FRW cosmological models      372
Dust, spherical gravitational collapse of      262
Earth, measuring the rotation rate      35 (box)
Eddington limit      see Accretion disks
Eddington Finkelstein coordinates      see Schwarzschild geometry
Einstein angle      see Gravitational lensing
Einstein equation      131 419 445 456459 482486
Einstein equation, as partial differential equations for metric      457
Einstein equation, compared with Newtonian field equation      452 (table)
Einstein equation, defined      483
Einstein equation, does not uniquely determine metric      457
Einstein equation, for FRW cosmologies      484
Einstein equation, for relativistic stars      537 (problem)
Einstein equation, linearized      see Linearized gravity
Einstein equation, Newtonian limit      485486
Einstein equation, number of independent component equations      457 484
Einstein equation, satisfies Bianchi identity      482
Einstein equation, schematic form      445 471
Einstein equation, vacuum      186 456459 471 483
Einstein equation, vacuum, Newtonian limit      460
Einstein tensor      see Curv ature
Einstein, A. and general relativity      4 107 131
Einstein, A. and special relativity      3 47 49
Einstein, A. on the origin of the equivalence principle      111
Electric charge      see Charge
Elements      see Nucleo-vnthesis
Embedding diagram      148152
Endstates of stellar evolution      see Stellar evolution
Energy density      348349 400
Energy, conservation of in flat spacetime      478479
Energy, density      474477
Energy, density, as a component of stress-energy      474
Energy, density, geometrized units      479
Energy, density, in a Newtonian gravitational field      342 345
Energy, density, in the short wavelength approximation      343
Energy, density, measured by an observer      477
Energy, flux equals momentum density      475
Energy, local conservation of in curved spacetime      480482
Energy, measured by an observer      98 154
Energy, no local density of in general relativity      342343
Energy, of a particle      87
Energy, total defined in asymptotically flat spacetimes      342
Energy-momentum Four-vector      87 also four-momentum
Energy-momentum tensor      see Stress-energy tensor
Eoetvoes experiments      107
Eoetvoes, R. von      107
Equality of accelerations in a gravitational field      see Equality of gravitational and inertial mass
Equality of gravitational and inertial mass      13 42 111
Equality of gravitational and inertial mass, connection with weightlessness      111
Equality of gravitational and inertial mass, tests      14(box) 107109
Equation of geodesic deviation      see Geodesic dev mtion. equation of
Equation of state      516 see ground radiation dust vacuum etc.
Equation of state, general properties      535
Equation of state, microscopic stability      535
Equation of state, summarized by stiffness parameter      525
Equation or equations      173n
Equivalence principle      110121 140
Equivalence principle, and clocks      113119
Equivalence principle, and local inertial frames      140
Equivalence principle, applies to all laws of phystes      113
Equivalence principle, Einstein on      111
Equivalence principle, how small a laboratorv is needed      120
Equivalence principle, implies light attracted by gravity      113
Equivalence principle, origin      111
Equivalence principle, rate difference between signal emission and reception      115119
Equivalence principle, rate explained by curved spacetime      126
Equivalence principle, rate explained by effect of gravity on clocks      125
Equivalence principle, rate in GPS      124
Equivalence principle, rate test      118 (box)
Equivalence principle, stated      113 119
Ergosphere      see Kerr geometry
Ether      48
Event      53
Event horizon      see Black holes
Exclusion principle      255 516520
Exclusion principle, and the structure of atoms      516
Exclusion principle, stated      516
Extremum, of a function      43
Extremum, of an action functional      43
1 2 3 4 5
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