523 Index aberration – radio galaxies, 174 – of starlight, 224 – Seyfert galaxies, 174 – relativistic, 140 – unified model of, 175 abundance adiabatic – 4He, 53, 60, 64 – expansion, 7, 10, 40 – 7Li, 66 – perturbations, 89, 103, 104, 127, – cosmic, 36, 43 499 – deuterium, 52, 59, 64 affine – hydrogen, 66 – connection, 303, 342, 361 – neutron, 54, 56 – geometry, 334 – of lightest elements, 62 – manifold, 342 – primordial, 49, 61, 63, 195 – parameter, 305, 373, 505 accretion, 171, 177 – space, 334 – characteristic temperature, 179 Aharonov–Bohm effect, 330 – disk, 180 Alfven´ wave, 172 – magnetohydrodynamic instabil- annihilation ity, 180 – electron–positron, 44 – viscous torque, 183 – gluon–gluon, 193 acoustic – particle–antiparticle, 10, 20, 42, – damping, 131 221 – oscillations, 12, 118, 129, 135, antenna 487, 503 – beam solid angle, 151 – peak at 150 Mpc, 105, 118 – collecting area, 151 – peaks, 130, 145 – effective aperture, 151 – waves, 88, 104, 144 – feedhorn, 153 action integral, 267, 273 – main beam, 150 active galactic nuclei, 79, 171 – power pattern, 150 – blazars, 173 – side lobes, 150 – – BL Lacertae, 174 – temperature, 152 – quasars, 172 antimatter Relativity, Astrophysics and Cosmology Radoje Beluseviˇ c´ Copyright c 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40764-4 524 Index – presence in the universe, 21, 43, – – ergosphere, 172 198 – – frame dragging, 172 astronomical unit (AU), 421 – supermassive, 170–172, 182, 187, atomic 190 – clock, 214, 250, 252 black-hole era, 198 – energy levels bolometer, 14, 153 – – conjectured by Boltzmann, 2 Boltzmann – – in cyanogen, 16 – constant, 8 – equation, 73, 504 baryon, 29, 37 – – for photons, 508, 509 – bulk velocity, 508 – factor, 50 – density, 22, 128 BOOMERANG telescope, 13, 148 – density parameter, 38 Bose–Einstein – loading, 512 – distribution, 508 baryon-number conservation, 198 boson, 21, 42 baryon-photon fluid, 512 – star, 192 baryon-to-photon density ratio, brightness 510 – distribution of the sky, 157 baryon-to-photon ratio, 66 – function, 508 basis – of blackbody radiation, 133 – anholonomic, 375 – temperature, 152 – coordinate, 336, 407 – dyad, 338 Cartan – holonomic, 380 – calculus, 342, 361 – one-form, 335 – formula, 364 – orthonormal, 380 – formulation of Newtonian grav- – tensors, 338 ity, 31 – vectors, 334 – structural equations, 377, 407 Bianchi identity, 300, 306, 313, 352 Cassini spacecraft, 183 – contracted, 315, 317 CBI telescope array, 15, 148, 153, – first, 374, 378 159 – second, 374, 379 CCD array, 416 Big Bang, 4, 28, 192 celestial binding energy – coordinates, 141 – 4He, 52 – equator, 160, 424 – deuterium, 51, 53 – sphere, 148, 165, 424, 475 – gravitational, 247 Cepheids, see stars – of lightest nuclei, 60 chemical Birkhoff’s theorem, 24, 257 – equilibrium, 38, 44 black hole, 163, 171, 198 – potential, 21, 42 – accretion, 182, 187 Cherenkov – rotating (Kerr) – radiation, 228 Index 525 Christoffel symbol, 275, 278, 293, conformal 295, 303, 376, 495 – mapping, 459 CMB, 4, 82 – time, 458 – angular power spectrum, 15, congruence of geodesics, 372 130, 137, 146 – connecting vector, 372 – dipole anisotropy, 121, 141 connection – discovery of, 10, 195 – coefficients, 294, 367, 368, 371 – energy density, 18, 36 – Koszul, 365 – foregrounds, 146, 147 – one-form, 376, 407 – lensing, 445, 478 continuity equation, 25, 85, 87, – map, 15, 149 122, 305, 324, 353 – multipole expansion, 135 contravariant – observational techniques, 146 – basis vectors, 270 – photons, 90 – components, 277, 296 – polarimeter, 485 – transformation rule, 277, 288 – polarization, 14, 81, 485, 489 convolution theorem, 158 – – (E,B)-type patterns, 487 coordinate transformations – – anisotropy, 478, 487 – Bardeen variables, 494 – – power spectrum, 480, 488 – gauge freedom, 491 – – WMAP measurement, 487 coordinates – primary anisotropies, 127 – Cartesian, 32, 89, 265, 278, 280, – secondary anisotropies, 131, 146 299, 347 – spectrum, 13 – celestial, 141 – temperature, 8, 12 – curvilinear, 240, 280 – – anisotropy, 142, 149, 157, 487 – galactic, 141 – – power spectrum, 15, 130, 137, – generalized, 265 143, 488 – spherical, 240 CMBFAST code, 105, 114 – system of, 334 co-moving Coriolis force, 282 – coordinates, 387, 458 correlation function, 107, 137 – distance, 412 cosmic – frame, 86, 387 – baryons, 67 – observer, 387, 390, 505 – dark age, 481 – wavevector, 88, 502 – energy density, 29 COBE telescope, 13, 148 – fluid, 130, 387, 395, 398, 489 collision rate, 37 – lens, 461 color index, 417 – photosphere, 11, 106, 195 Compton – rays, 213 – scattering, 12 – shear, 468, 471 – – inverse, 132, 436 – time, 6, 9, 30, 387, 439 configuration space, 265 – variance, 138, 139, 488 526 Index cosmic expansion covariant – accelerated, 27, 196, 398, 402, 443 – basis vectors, 269 – decelerated, 395, 443 – components, 270, 271, 277, 296 – deceleration parameter, 391 – derivative, 296, 308, 366 – scale parameter, 7 – formulation, 232 cosmic inflation, 514 – tensor, 290 – chaotic, 517 – transformation rule, 277, 288 – density perturbations, 517 Crab Nebula, 207 – quantum fluctuations, 514 critical density, 29, 396 – reheating, 516 curvature – scalar field φ, 514 – extrinsic, 311 – slow-roll approximation, 516 – forms, 361 cosmic microwave background, – intrinsic, 302, 307, 311, 330 see CMB – of manifold, 331 cosmological – of spacetime, 35, 111, 253, 319, – constant, 27, 30, 104, 142, 401, 396 402, 440, 515 – parameter, 27, 30 – fluctuations – perturbations, 489, 494, 518 – – acoustic dynamics, 509, 511 – radius of, 397 – – adiabatic, 499 – scalar, 496 – – dust-dominated universe, 501 – tensor, 369 – – Einstein equations, 495 cyanogen excitation, 17 – – gauge transformation, 491 cyclotron frequency, 234 – – Newtonian theory, 82 – – radiation-dominated universe, d’Alembertian, 299 503 dark energy, 30, 196, 402 – – relativistic theory, 489 dark halo, 77, 101 – – scalar, 491 dark matter, 29, 77, 92, 96, 103, – – tensor, 491 104, 162 – – tight-coupling limit, 510 dark-sky paradox, 17 ––vector,491 DASI telescope array, 14, 148, 159, – hypothesis, 4, 82, 86 485 – parameters, 142 de Broglie Coulomb – wavelength, 9 – barrier, 52 Debye – force, 21 – length, 23 – potential, 23 – shielding, 21 – scattering, 235 degenerate covariance – era, 198 – matrix, 158 density – of tensors, 288 – contrast, 87, 106 – energy, 39 Index 527 – fluctuations, 106 – tensor, 316, 382, 406, 496 – number, 39 Einstein, Albert, 316 – parameter, 29 Einstein–de Sitter model, 89, 123 – phase-space, 55 electromagnetic detailed balance, 54, 74 – four-potential, 272 differential forms, 342 electromagnetic field – coderivative operator, 354 – tensor, 273 – exterior derivative, 343, 349 electroweak – Hodge star operator, 347 – symmetry, 192 – inner product, 358 ellipse, 465 – interior product, 363 ensemble – one-form, 333, 342 – average, 108, 137, 138, 487 – two-form, 343, 377, 408 – average power, 109 – wedge product, 344 entropy differential geometry, 331 – conservation of, 7, 42 Dirac – density, 22, 40, 41 – delta function, 109 equinox, 423 – monopole, 330 equivalence principle, 247 directional derivative, 332 – strong, 247 distance modulus, 415, 424, 427, – weak, 247 440 ergodic hypothesis, 108, 138 distribution function, 38, 45, 508 ether, 204, 215, 228, 229 Doppler effect, 97, 129, 134, 140, Euclidean 220, 221, 226, 249, 262 – geometry, 394 dual field tensor, 306, 353 – space, 25, 27, 31, 239, 299, 333 Euler’s equation, 25, 85, 87, 324 ecliptic Euler–Lagrange equations, 265 – coordinates, 456 extragalactic distance – definition of, 424 – angular-diameter distance, 413, – latitude, 223 449 – plane of, 224, 423 – co-moving distance, 412 Eddington – distance ladder, 420 – limit, 178 – expanding photosphere method, Einstein 434 – field equations, 320, 496 – fundamental plane relation, 432 – – conservation laws, 319 – fundamental rung, 427 – – coordinate transformations, – luminosity distance, 412, 419, 317 440 – – for empty space, 316 – primary indicator, 435 – – from variational principle, 324 – proper distance, 389 – – weak-field limit, 320 – summation convention, 239, 271 528 Index – secondary indicator, 426, 427, – winds, 188 432, 438 galaxy – to Large Magellanic Cloud, 426 – Andromeda, 28, 165 – Tully–Fisher relation, 123, 430 – biasing, 119 – classification, 168 Fermat’s principle, 253, 269 – correlation function, 105, 107 fermion, 21, 42 – dwarf, 98, 159 Feynman – elliptical, 98, 159, 169, 188 – path integral approach, 325 – irregular, 170 first stars, 77, 195 – lenticular, 169 Fizeau’s experiment, 229 – Local Group, 141, 165 flux – Magellanic Clouds, 165 – definition of, 413 – Milky Way, 121, 160, 189 – of angular momentum, 184 – morphological evolution, 187 flux density, 399, 413 – nonlinear evolution, 119 – incident on antenna, 150 – peculiar motion, 121 – of starlight, 414 – redshift distortions, 121 Foucault pendulum, 302 – – finger-of-God effect, 126 Fourier – rotation curve, 97 – decomposition, 135 – Sombrero, 170 – modes, 108, 110 – spiral, 97, 168, 188 – series, 88 – spiral arms, 160, 168 – space, 108 – starburst, 188 – transform, 109, 157 – Whirlpool, 170 Fresnel drag coefficient, 229 galaxy cluster, 98, 195 Friedmann–Lemaˆıtre – Abell 2029, 99 – equations, 27, 387, 395, 406, 410, – Centaurus, 141 500 – Coma, 165 – – derivation of, 402 – Virgo, 124, 165 – model, 4, 82, 459, 475 galaxy redshift survey – universe, 27, 395, 407, 440, 472 – 2MASS, 167 fusion – 2dFGRS, 83, 115 – Gamow – CfA, 116 – – condition, 37 – DEEP2, 116 – SDSS, 115 galactic Galilean relativity, 203 – bulge, 160 Galilei, Galileo, 162 – center, 160 gamma-ray – disk,