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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

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Предметный указатель
Laws of physics in external gravitational fields      89ff
Leibniz rule      10 30
Lense — Thirring effect      see also “Precession of gyroscope” 263 265
Levi — Civita connection      58
Levi — Civita connection, local expression of      58
Lie algebra of vector fields      17 71
Lie derivative      21 24 71
Lie derivative, local coordinate expression of      25 71
Lie derivative, of metric tensor      139
Lie transport      115 124—125
Light rays deflection of      86
Light rays deflection of measurements of      180—181
Light rays deflection of, by the solar corona      181—182
Light rays deflection of, in a Schwarzschild metric      178ff
Light rays in geometrical optics      103
Light rays puths of      90
Linear connection      see “Affine connection”
Linearized Bianchi identities      214
Linearized Einstein tensor      214
Linearized field equations      215 217—218
Linearized field, multipole expansion of      226ff
Linearized Ricci tensor      214 217
Linearized Riemann tensor      223
Linearized theory gravitational waves in      220ff
Linearized theory of gravity      214ff
Local basis of one-forms      21
Local basis of vector fields      21
Local coordinate neighborhood      4
Local coordinate systems      12 118—119
Local flow of vector field      21
Local inertial system      83 89 147
Local Lorentz transformation      147 151
Local one-parameter group      22
Local reference frames      111ff
Locally finite covering      43
Lorentz gauge condition      102
Lorentz invariance, local      151
Lorentz manifold      88
Lorentz manifold, spherically symmetric      see also “Manifolds Pseudo-Riemannian” 88
Lorentz transformation      147
Lorentz transformation, local      147 151
Magnetic dipole radiation      see also “Pulsars” 352
Magnetic fields conservation of magnetic flux      350
Magnetic fields determined with cyclotron line      348—349
Magnetic fields diffusion time      350
Magnetic fields influence on neutron star cooling      319
Magnetic fields matter in strong magnetic fields      358—360
Magnetic fields of neutron stars      348—349 353
Magnetic fields rapid dissipation      350
Magnetic fields reconnection      350
Magnetic fields relativistic magnetohydro-dynamics      351—352
Magnetosphere of pulsar      355—358
Manifold      4ff
Manifold $\sigma$-compact      4
Manifold (pseudo-)Riemannian      20
Manifold differentiable      6
Manifold dimension of      12
Manifold flat      68
Manifold locally flat      4
Manifold open      5
Manifold orientable      36
Manifold oriented      36
Manifold paracompact      4
Manifold product      8
Manifold Schwarzschild — Kruskal      196
Manifold sub-      7
Manifold topological      4 12
Mappings and tensor fields      22
Mappings coordinate representation of      6
Mappings differentiable      6
Mappings of class $C^{\infty}$      56
Mass function for binary systems      382
Material derivative      432
Matter in strong magnetic fields      358—360
Matter in strong magnetic fields, ground-state energy of hydrogen atom      360
Maximal mass of neutron stars      300
Maximal mass of neutron stars, for realistic equations of state      298
Maximal mass of neutron stars, model independent bounds      299 305
Maxwell's equations      93
Maxwell's equations, as variational equations      144
Maxwell's equations, characteristics of      165
Maxwell's equations, conformal invariance of      94
Mean free path and diffusion constant      343
Mean free path of neutrino during supernova formation      342
Mean free path of neutrino in neutron star      307
Measure-valued one-form      45
Mechanics of binary systems      374—376 382—383
Mechanics of binary systems, mass function      382
Mechanics of binary systems, motion of test particle      375
Mechanics of binary systems, motion of test particle, equilibrium positions      375
Mechanics of binary systems, motion of test particle, equipotential surfaces      375
Mechanics of binary systems, motion of test particle, inner Lagrange point      376
Mechanics of binary systems, motion of test particle, Jacobi integral      375
Mechanics of binary systems, motion of test particle, nature of critical points      376
Mechanics of binary systems, motion of test particle, Roche lobe      376
Mechanics of binary systems, Navier — Stokes equation in corotating system      376
Mechanics of binary systems, velocity curve      383
Melting temperature of ion lattice      310
Metric conformally flat      134—135
Metric connection      57 63
Metric Lorentzian      88
Metric physically equivalent      139
Metric pseudo-Riemannian      19
Metric raising and lowering indices with      59
Metric Riemannian      see also “Kerr-Newman metric; Post-Newtonian approximation; Schwarzschild metric; Weak field approximation” 19
Mini-black holes      369
Mobius strip      36
Motion of a test body      see “Test body”
Moving frame      see also “Tetrad field” 61
Multilinear forms      27
Multilinear mapping, associated to tensor field      19
Multilinear mapping, associated to tensor field, differential forms      29
Multipole expansion of linearized field      226ff
Naked singularity      365
Navier — Stokes equation nonrelativistic      434
Navier — Stokes equation relativistic      426 440
Neutral current interaction      313
Neutral current interaction, and neutrino scattering      342
Neutral current interaction, effect in pair annihilation      335—336
Neutral current interaction, effective four-fermion interaction      314 342
Neutrino emission from neutron stars gradient of neutrino luminosity      307
Neutrino emission from neutron stars influence of superfluidity      318
Neutrino emission from neutron stars modified Urea rate      314—316
Neutrino emission from neutron stars modified Urea reactions      313
Neutrino emission from neutron stars neutrino pair bremsstrahlung      313
Neutrino emission from neutron stars neutrino transparency      307
Neutrino emission from neutron stars nucleon pair bremsstrahlung      313
Neutrino emission from neutron stars pion condensate $\beta$-decay      317
Neutrino emission from neutron stars suppression of Urea reactions      see also “Cooling of neutron stars” 313
Neutrino emission from supernovae      305
Neutrino emission from supernovae neutronization reactions      342
Neutrino emission from supernovae, neutrino trapping      342—344
Neutrino emission from supernovae, thermal reactions      see also “Supernova formation; Core collapse” 305 334 345
Neutrino emission of massive stars      334
Neutrino emission of massive stars, important processes      334
Neutrino emission of massive stars, luminosity      333 336
Neutrino emission of massive stars, pair annihilation      334—336
Neutrino opacity      342
Neutrino scattering on heavy nuclei      342—343
Neutrino scattering on neutrons      343
Neutrino stars      297
Neutrino stars Oppenheimer — Volkoff limit for      297
Neutrino trapping      342—344
Neutron stars      280ff
Neutron stars allowed core region      302
Neutron stars and supernovae      281 285 306 346
Neutron stars bounds for muss      189 305
Neutron stars central core      294
Neutron stars cooling of      see “Cooling of neutron stars crust” 293—294
Neutron stars cyclotron lines      348—349
Neutron stars density profile      298
Neutron stars, detailed models      297
Neutron stars, equations of state      297
Neutron stars, Fermi momenta of nucleons      309
Neutron stars, formation      281 285 346
Neutron stars, gross features      285
Neutron stars, historical remarks      285
Neutron stars, hyperons in      294
Neutron stars, ideal n-p-e model      394
Neutron stars, inner fluid      294
Neutron stars, interior      293
Neutron stars, magnetic fields      348—349 353
Neutron stars, mass-radius relation      297
Neutron stars, maximum mass      296 298—299 305
Neutron stars, observations comparison with cooling calculations      318—321
Neutron stars, observations cyclotron lines      348—349
Neutron stars, observations masses      269 379
Neutron stars, observations radii      381
Neutron stars, observations surface temperatures      306
Neutron stars, observations thermal radiation      see also “Binary pulsar; Pulsars; X-ray binary bursters; X-ray binary pulsars” 306
Neutron stars, Oppenheimer — Volkoff model      296
Neutron stars, pion condensate      294 316
Neutron stars, quark phase in      294
Neutron stars, relation between surface and interior temperature      308
Neutron stars, specific heat      308 312
Neutron stars, superconductivity in      294 311
Neutron stars, superfluidity in      294 310 318
Neutron stars, temperature profile      308
Neutron stars, thermal energy transport      307
Neutron stars, thermal equilibrium      306—307
Neutron stars, thermodynamic properties      306ff
Neutron stars, uniform density model      see also “Accretion; Binary pulsar; Pulsars Superfluidity 290 318
Neutronization      see also “Electron capture” 280
Newton vs. Coulomb      327
Newtonian limit      96—97 133
Newtonian limit, potential      126 128
Newtonian limit, theory, comparison with      126
Nonsaturation of gravitational forces heuristic discussion      324
Nonsaturation of gravitational forces rigorous results      325—327
Normal coordinates      50
Nova outbursts      387
Nuclear density      295 310
Nucleon-nucleon interaction BCS pairing      311—312
Nucleon-nucleon interaction in nucleon pair bremsstrahlung      314—315
Nucleon-nucleon interaction Landau interaction      316
Nucleon-nucleon interaction Landau limit      316
Nucleon-nucleon interaction one pion exchange      315
Nucleon-nucleon interaction short range contribution      315
Number density of baryons      289 307
Observer at rest      107
Observer rotation of      120
One parameter group local      22
One parameter group of diffeomorphisms      22
One-forms      19
One-forms, covariant derivative of      53
One-forms, pull back of      19
Opacity      307 408
Opacity Rosseland-mean      408
Opacity, electron scattering      408
Opacity, free-free transitions      408
Orientation and volume forms      36
Orientation induced      44
Orientation of boundary      44
Orientation of manifold      36
Orientation same      36
Oriented atlas      36
Oriented basis of one-forms      39
Oriented manifold      36
Palatini identity      217
Parallel transport      50—51
Parallel transport, path independence of      69
Penrose mechanism      368
Perihelion (periastron)      see also “Binary pulsar; Post-Newtonian approximation”
Perihelion (periastron) advance of      176ff 220 258 268
Perihelion (periastron) advance of, of mercury      178
Perturbations adiabatic      291 338
Perturbations eigenvalue equation for      291
Perturbations of thin accretion disks      419
Photodisintegration      280
Photodisintegration, of iron-nickel core      280 337—338
Photospheric boundary conditions      307
Pion condensation      294 316
Pion condensation quasiparticles in presence of      317
Pion condensation, chiral rotation      317
Pion condensation, influence on neutron star cooling      306 318 320
Pion condensation, wave vector      317
Plane waves in the linearized theory      221ff
Plane waves in the linearized theory, polarization states of      222
Plane waves in the linearized theory, polarization tensor of      221
Planetary orbits      273ff
Plasma frequency      310
Poincare lemma      33 40 71
Polarization states of gravitational waves      222
Polarization tensor for the linearized field      221
Polarization vector of electromagnetic waves      101
Positive chart      36
Positive coordinate system      37
Post-Newtonian approximation asymptotic fields      252
Post-Newtonian approximation Christoffel symbols      248
Post-Newtonian approximation equation of motion      255
Post-Newtonian approximation field equations      246
Post-Newtonian approximation gauge conditions for      244 247 251
Post-Newtonian approximation metric      254
Post-Newtonian approximation periastron shift      258
Post-Newtonian approximation precession of gyroscope      261
Post-Newtonian approximation Ricci tensor      245
Post-Newtonian approximation two-body problem      256
Post-Newtonian approximation two-body problem, center of mass in      256
Post-Newtonian approximation two-body problem, Hamilton — Jacobi function of      260
Post-Newtonian approximation two-body problem, Hamiltonian for      257—258
Post-Newtonian approximation two-body problem, solution of      258
Post-Newtonian potentials      247
Post-Newtonian potentials, for system of point particles      254
Post-Newtonian potentials, particle in      249
Post-Newtonian potentials, particle in, Langrangian for      249
Potential effective      174 176
Potential electromagnetic      93ff
Potential gravitational inertial      88
Potential Newtonian      126 128 219
Precession of gyroscope geodesic precession      186ff 263 265
Precession of gyroscope in a gravitational field      111ff 115
Precession of gyroscope in a Schwarzschild field      186ff
Precession of gyroscope in orbit around the Earth      263
Precession of gyroscope in post-Newtonian approximation      261—263
Precession of gyroscope Lense — Thirring effect      263 265
Principle of equivalence      79 81ff 135
Principle of equivalence, ambiguities      95
Principle of equivalence, mathematical formulation      87
Principle of general covariance      see “Covariance”
Product manifold      8
Product manifold, differentiable structure of      8
Pseudo-Riemannian manifold      20
Pseudo-Riemannian metric      19
Pseudotensors and three-forms of stress-energy      see also “Energy and momentum; Superpotential”
Pseudotensors and three-forms of stress-energy for a plane wave      236—237
Pseudotensors and three-forms of stress-energy for gravitational field      155
Pseudotensors and three-forms of stress-energy Landau — Lifschitz      155—156
Pull back of covariant tensor field      20 22
Pull back of one-form      20
Pulsars      see also “Binary pulsar; Crab pulsar; Supernovae”
Pulsars, aligned rotator model      355 357
Pulsars, as rotating neutron stars      352
Pulsars, braking index      353
Pulsars, characteristic age      353
Pulsars, energy in radio pulses      354
Pulsars, gravitational radiation from      354
Pulsars, induced electric fields      355 357
Pulsars, instability of exterior vacuum solution      355—357
Pulsars, light cylinder model      358
Pulsars, magnetic dipole radiation      352—353
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