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Straumann N. — General relativity and relativistic astrophysics
Straumann N. — General relativity and relativistic astrophysics



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Название: General relativity and relativistic astrophysics

Автор: Straumann N.

Аннотация:

This book divides into three parts. Part I develops the mathematical tools used in the general theory of relativity. Since I wanted to keep this part short, but reasonably self-contained, I have adopted the dry style of most modern mathematical texts. Readers who have never before been confronted with differential geometry will find the exposition too abstract and will miss motivations of the basic concepts and constructions. In this case, one of the suggested books in the reference list should help to absorb the material. I have used notations as standard as possible. A collection of important formulae is given at the end of Part I. Many readers should start there and go backwards, if necessary.


Язык: en

Рубрика: Физика/Гравитационное взаимодействие/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1984

Количество страниц: 459

Добавлена в каталог: 02.10.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute derivative      see “Covariant derivative”
Absolute exterior differential      65
Acceleration      see also “Fermi-transport; Geodesic deviation” 113 118 120
Accretion as source of x-rays from compact objects      201 378 382 388
Accretion in x-ray binary bursters      380
Accretion in x-ray binary pulsars      377—378
Accretion onto black holes and neutron stars      388ff
Accretion rate      378 388 391
Accretion rate critical      414
Accretion tori      see also “Spherical accretion onto black holes; Disk accretion” 432
Action Einstein — Hilbert      148
Action principle of least      see “Variational principle”
Adiabatic index      280 337—338
Adiabatic index, critical value for radial stability      337—338
Adiabatic index, during supernova formation      337
Affine connection      47
Affine connection, curvature of      54
Affine connection, induced      47
Affine connection, metric      57 63
Affine connection, torsion of      54
Alfven radius      377
Alternation operator      27
Angular momentum of black holes      363
Angular momentum of isolated systems      156—157
Antiderivation of differential forms      30
Asymptotic fields in post-Newtonian approximation      252
Asymptotic fields of isolated systems      229
Asymptotic fields of Kerr — Newman black holes      362—363
Asymptotically flat space-time      154
Asymptotically flat space-time angular momentum of      156f 230ff
Asymptotically flat space-time energy and momentum of      146 154ff 229ff
Atlas      4
Atlas differentiable      5
Atlas maximal      5
Atlas oriented      36
Autoparallel along curve      49
Background geometry      217
Basis of p-forms      28
Basis of tangent space      13
Basis of vector space of derivations      11
Basis oriented      39
Bernoulli equation      390 393 435
Bernoulli equation nonrelativistic      435
Bernoulli equation relativistic      390
Beta-equilibrium      294—295
Beta-equilibrium and Urea process      313
Beta-equilibrium for ideal mixture      295
Bianchi identities      56 60 64 66 73
Bianchi identities as constraint equations      161
Bianchi identities contracted, reduced      60—61 128 132 152
Bianchi identities, derivation and meaning of      138—139
Bianchi identities, linearized      214
Binary pulsar PSR1913+16      240 258 261 264 266
Binary pulsar PSR1913+16 advance of periastron      268
Binary pulsar PSR1913+16 arrival time data      266
Binary pulsar PSR1913+16 arrival time data analysis of      267
Binary pulsar PSR1913+16 change of period      268
Binary pulsar PSR1913+16 change of period and gravitational radiation      240 270
Binary pulsar PSR1913+16 change of period and viscous dissipation      276
Binary pulsar PSR1913+16 companion      271—276
Binary pulsar PSR1913+16 companion, mass of      269
Binary pulsar PSR1913+16 discovery      266
Binary pulsar PSR1913+16 dispersion measure      267
Binary pulsar PSR1913+16 distance      267
Binary pulsar PSR1913+16 important parameters      268—269
Binary pulsar PSR1913+16 mass      269
Binary pulsar PSR1913+16 orbital period      266
Binary pulsar PSR1913+16 orbital phase shift      270
Binary pulsar PSR1913+16 pulse period      266
Binary pulsar PSR1913+16 relativistic effects      268
Binary pulsar PSR1913+16 self-consistency of post-Newtonian parameters      270
Binary pulsar PSR1913+16 spin precession      264 269
Binary x-ray pulsars      see “X-ray binary pulsars”
Binary x-ray sources      see “X-ray binaries”
Birkhoff theorem      169 198
Birkhoff theorem, generalized      211
Black holes angular momentum parameter      363
Black holes approach to stationary state      361 372
Black holes area of horizon      369
Black holes charge of      363
Black holes Cygnus X-l      372 382
Black holes effective potential for test particle      174 176
Black holes ergosphere      366
Black holes extraction of rotational energy      368
Black holes g-factor      364
Black holes horizon      197 200 367—368
Black holes identifying compact objects as      201 299 372 382 385
Black holes inevitability of collapse to black hole      82 189
Black holes Kerr      362
Black holes Kerr coordinates      367
Black holes Kerr — Newman      362
Black holes Kruskal coordinates      193 195 197
Black holes miniholes      369
Black holes naked singularity      365
Black holes nonrotating (“Bardeen”) observers      365
Black holes parameters for stationary solutions      362—363
Black holes Reissner — Nordstram      172 207
Black holes rigid rotation of horizon      366
Black holes rotating      361 363
Black holes Schwarzschild      169 195ff 200—201
Black holes singularity      197 200 367
Black holes special cases      362
Black holes spontaneous radiation of      369
Black holes trapped surface      see also “Accretion on black holes; Gravitational collapse; Kerr — Newman metric; Schwarzschild; Reissner — Nordstram solution 371
Black holes “no hair” theorem      361 372
Bremsstrahlun absorption coefficient      408
Bremsstrahlun electron-electron      398
Bremsstrahlun electron-ion      397—398
Bremsstrahlun spectral emissivity      397
Bremsstrahlun total emissivity      398
Bremsstrahlung      397 408
Cartan calculus      27
Cauchy data      160 162—163
Cauchy development      160
Cauchy development local existence      161—162
Cauchy development stability of      371
Cauchy Lemma      433
Cauchy problem      160
Cauchy surface      160
Cauchy traction      433
Causal structure      171 192 195ff
Chain rule      10
Chandrasekhar limit      283 329 337 341 346
Chandrasekhar limit historical remarks      283
Characteristic surfaces of a differential equation      164
Characteristic surfaces of Einstein's field equations      163ff
Characteristic surfaces of Maxwell's vacuum equations      165
Characteristic surfaces of the generalized wave equation      163—164
Chart      4
Chart, domain of      4
Chart, positive      36
Christoffel symbols      48 61 90
Christoffel symbols, along a path      118
Christoffel symbols, transformation law for      48
Class $C^{\infty}$      5
Class $C^{\infty}$ differentiable manifold      5
Class $C^{\infty}$ function on $\mathds{R}^{n}$      5
Class $C^{\infty}$ function on manifold      6
Class $C^{\infty}$ mapping      6
Codazzi — Mainardi equation      162
Codifferential      40 42 46 72 94
Codifferential coordinate expression of      40 72
Commutator of derivations      16
Commutator of vector fields      16 24 71
Compact x-ray sources      see “X-ray binaries”
Complete tensor algebra      24
Complete vector field      22
Components of affine connection      48
Components of differential forms      30
Components of tensor field      18
Components of vector field      15
Components transformation law of      15 18
Comptonization      408
Conductivity electrical      349 380
Conductivity thermal      308
Conformal invariance of scalar wave equation      95
Conformal invariance of source-free Maxwell equations      95
Conformal metrics      94
Conformally flat manifold      87
Conformally flat theory      134
Congruence of timelike geodesics      124
Connection coefficients      see also “Connection forms” 48
Connection forms      61 72 147 162 209
Connection forms of a spherically symmetric field      167 209
Connection forms transformation properties of      65 147
Conservation law, associated to a Killing Held      146 174
Conservation of angular momentum      156—157
Conservation of electromagnetic current      93
Conservation of energy and momentum      91 154ff
Cooling of neutron stars      305ff
Cooling of neutron stars, comparison with observations      320
Cooling of neutron stars, cooling curves      318—321
Cooling of neutron stars, early versus late phases      305—306
Cooling of neutron stars, effects of general relativity      319
Cooling of neutron stars, neutrino emissivities      313
Cooling of neutron stars, observations      306
Cooling of neutron stars, role of magnetic fields      319
Cooling of neutron stars, specific heat      312
Cooling of neutron stars, temperature distribution      308
Cooling time      318
Cooling time, role of pion condensate      see also “Neutron stars; Neutrino emission from neutron stars” 319 321
Coordinate representation of codifferential      40 72
Coordinate representation of covariant derivative      54 72
Coordinate representation of differential form      29
Coordinate representation of exterior differential      33
Coordinate representation of function      12
Coordinate representation of Lie derivative      25 71
Coordinate representation of star operation      38
Coordinate representation of tangent mapping      13
Coordinate representation of tensor field      15
Coordinate representation of vector field      15
Coordinate transformation      5
Coordinate transformation, infinitesimal      216
coordinates      4
Coordinates, change of      5
Coordinates, Eddington — Finkelstein      198ff
Coordinates, for Schwarzschild solution      see “Schwarzschild”
Coordinates, Gaussian      50
Coordinates, harmonic      161 228
Coordinates, local      12
Coordinates, normal      50 130
Coordinates, of a point      4
Coordinates, singularity      171 190
Coordinates, traceless transverse (TT)      224
Copernical frame      111 116
Copernical frame, rotation of a      116
Core collapse      281 330 338
Core collapse neutronization      342 345
Core collapse neutronization as trigger      337 341
Core collapse photodissociation as trigger      see also “Supernova formation” 280 337—338
Core collapse, adiabatic nature      344 348
Core collapse, conditions at onset of      280 345
Core collapse, core bounce      342 347
Core collapse, dynamical time scale      344
Core collapse, dynamics of collapse      338
Core collapse, entropy generation during collapse      342 344 348
Core collapse, homologous core mass      341
Core collapse, homologous nature      338—341
Core collapse, inevitability of collapse      337
Core collapse, models of type II supernovae      330
Core collapse, neutrino trapping      342—344
Core collapse, persistence of heavy nuclei      344
Coriolis force      121
Cosmic censorship conjecture      201 371
Cosmological constant      133—134
Cotangent space      17
Covariance general      88
Covariance with respect to K(M)      88 151
Covariant derivative      49
Covariant derivative, along a curve      49
Covariant derivative, and exterior derivative      35
Covariant derivative, and parallel transport      50 52
Covariant derivative, as a derivation of the tensor algebra      52
Covariant derivative, local expression of      54 72
Covariant derivative, of tensor fields      51 53
Covariant derivative, of vector fields      49
Covariant tensor algebra      23
Covariant tensor field      20
Crab Nebula      281 354—355
Crab nebula, energy spectrum of electrons in      354
Crab nebula, magnetic fields in      354
Crab nebula, synchrotron lifetime of electrons      354—355
Crab nebula, synchrotron radiation from      354
Crab pulsar      281 306 353—355
Curvature forms      62 73
Curvature forms, dual      153
Curvature forms, of a spherically symmetric field      168 210
Curvature forms, transformation properties of      66 147
Curvature of affine connection      54
Curvature tensor      54
Curvature tensor symmetry properties of      58 60
Curvature tensor, components of      55
Curvature tensor, physical meaning of      123ff
Curve covariant derivative along      49
Curve differentiable      21
Curve geodesic      50
Curve integral      21
Curve maximal integral      21
Cyclotron line spectroscopy      348—349
Cygnus X-l      202 372 374 382 388
Cygnus X-l as a black hole candidate      202 382 385
Cygnus X-l distance      384
Cygnus X-l general properties      382—383
Cygnus X-l likely mass      385
Cygnus X-l lower limit to mass      383—385
Cygnus X-l luminosity      382
Cygnus X-l mass function      383
Cygnus X-l optical companion      382
Cygnus X-l orbital parameters      382—383
Cygnus X-l time variability      382
Cygnus X-l x-ray spectrum      382
d'Alembertian      95
Dark matter in galaxies      297
Dark matter in galaxies, neutrinos as      297
Debye function      311
Debye heat capacity      311
Debye temperature      311
Deflection of light rays      see “Light rays”
Deformation tensor      432
Derivation induced      31
Derivation local      30
Derivation of algebra of smooth functions      16
Derivation of differential forms      30
Derivation of function with respect to vector-field      16
Derivation of germs of functions      10
Derivation restriction of      31
Diffeomorphism      5 6
Differentiable manifold      see “Manifold”
Differentiable structure      6 8
Differentiable structure class $C^{\infty}$      5
Differentiable structure, inequivalent      6
Differentiable structure, of product manifold      8
Differential forms      27 29
Differential forms antiderivation of      30
Differential forms, closed      33
Differential forms, components of      30
Differential forms, derivation of      30
Differential forms, exact      33
Differential forms, exterior derivative of      32 35 71
Differential forms, induced mapping of      30
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