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Cambridge University Press 978-1-107-03731-1 - General Relativity and Gravitation: A Centennial Perspective Edited by Abhay Ashtekar (Editor in Chief), Beverly K. Berger, James Isenberg and Malcolm Maccallum Index More information

Index

apparent horizons, 352, 358, 364 CDM, 166, 172, 191, 201, 206, 592 area gap, 574, 581, 586, 595 δN formalism, 189–192 area theorem, 28, 142, 614, 618 δN formula, 186 asymptotic flatness, 41, 412, 466 μ-type distortion (of CMB spectrum), 196 asymptotic quantization, 506 σ constant, 486 asymptotic safety, 504–508, 556–567 r-modes, 108 asymptotically flat initial data, 454 2dF survey, 170, 195 asymptotically flat initial data set, 418 asymptotically simple spacetimes, 422 acceleration of the Universe, 35, 166, 659 Atacama Cosmology Telescope, see ACT accretion, 135, 140, 143 averaging problem, 223, 227 disk, 28, 137, 138, 140, 155 AVTD behavior, 450 magnetized, 142 maser radiation, 137 B-mode polarization, 7, 170, 173, 182, 211, 215, 239, acoustic oscillation, 203–205 289, 334 damping, 204 back reaction, 223, 228 ACT, 163, 195, 206 background independence, 555–557, 595, 596 active galactic nuclei, 121, 134, 135, 143, 156, 157 & n-point functions, 597–600 structure resolved by microlensing, 118 & quantum geometry, 571–574 adaptive mesh refinement, 368, 372 BAO, 7–9, 170–171 ADM angular momentum, 622 Bartnik and McKinnon sequence, 377 ADM energy, 418, 419, 423 Bartnik mass, 432 ADM formulation, 18, 297–299, 364, 366, 413, 423, baryon acoustic oscillation, see BAO 433, 443, 569, 570, 593 BATSE, 148 ADM mass, 429, 467, 595, 596, 614, 621, 622, 631 beaming angle, 152, 153 ADM momentum, 423, 424, 595 Bel–Robinson energy functionals, 489 ADM-York formulation, 366 Bel–Robinson tensor, 461, 466 AdS/CFT correspondence, 368, 389, 394, 506–510, Beppo-SAX, 148, 152 647–658 Bianchi identities, 11, 16, 476, 491, 628 & black hole entropy, 650 Bianchi models, 13, 36, 224–225, 487, 490, 585, 587, & condensed matter, 656 591 & hydrodynamics, 656 orthogonal, 224 & quantum black holes, 654 tilted, 224 & quark confinement, 655 biasing, 130, 171 status of, 652–654 BICEP2, 7, 169, 182, 193, 211, 218, 242, 289 Advanced LIGO (aLIGO), 7, 250, 251, 281 big bang nucleosynthesis, 33, 35, 78, 162, 165, 224, Advanced Virgo, 250, 251, 281 331 algebraic approach to quantum field theory, 519 binary black hole problem, 364 almost-EGS theorem, 223 binary mergers, 150

© in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-03731-1 - General Relativity and Gravitation: A Centennial Perspective Edited by Abhay Ashtekar (Editor in Chief), Beverly K. Berger, James Isenberg and Malcolm Maccallum Index More information

668 Index

binary neutron stars, 383 Cherenkov Telescope Array, 157 binary pulsar, 4–6, 42, 80, 87, 90, 91, 289, 297 Christoffel relations, 13 BKL conjecture, 357, 398, 450 classical tests, 4 black hole, 4, 5, 10, 28, 469 closed timelike lines, 17 entropy, 511, 592–597, 642–647 CMB, 5, 162 evaporation, 596, 597, 605, 643, 646, 647, 655 anisotropy, 198–209 fundamental plane, 143 dipole, 198–199 intermediate, 141 primordial, 200–206 non-uniqueness, 618 polarization, 209–215 perturbation theory, 378 correlations, 211 stellar, 29, 133, 138–140, 143 power spectrum, 205 mass, 138–140 spectrum, 196–198 spin, 140–141, 144, 155 distortions, 196–198 supermassive, 29, 133, 135–137, 143, 148, 155, CMC, see constant mean curvature 156, see also supermassive binaries, see COBE, 163, 176, 195, 199 also supermassive black hole mergers cold spot, 202, 210, 211, 225 mass, 135, 137 compact hyperbolic manifolds, 482 size, 135, 136 compact star, 148 stellar orbits, 137 compact-object binaries, 154, 155, 311–313, 317–322 black hole scattering problem in 5d, 390 compactifications, 616 black hole–neutron star binaries, 149, 154, 155, 384 Compton Gamma Ray Observatory, see CGRO black membrane, 624 Compton scattering, 197 black rings, 392, 438, 620–647 computer algebra, 5 black Saturn, 392, 622 concordance model, 7, 35, 165 black strings, 392, 616–619 conformal class, 484 blow-up phenomena, 416 conformal curvature, 15–16 Bondi mass, 429 conformal intrinsic geometry, 455 boson stars, 365, 374 conformal Killing operator L, 414 Bowen–York data, 364 conformal method, 414 branes, 167 conformally flat near infinity, 419 break-down criterion, 459 congruences bremsstrahlung, 197 null, 14 Brown–York mass, 426 timelike, 14 Brownian motion, 3 connected sum, 481 BSSN formalism, 364, 366 connection dynamics, 569, 571, 572, 576, 586, 593, bubble collisions, 180–181 603 bubbles, 400 constant mean curvature, 415 bullet cluster, 128 hypersurfaces, 485 constraint damping, 367 Cadeˇˇ z coordinates, 363 constraint equations, 18, 413, 454 Callan, Giddings, Harvey, Strominger (CGHS) continuously self-similar, 371 two-dimensional spacetimes, 399 continuum limit, 565, 567, 581–583 Cauchy formulation, 366 core-collapse supernovae, 149, 153, 386 Cauchy horizon, 472 Cosmic Background Explorer, see COBE Cauchy problem, 453 cosmic censorship conjecture, 364, 371, 388, 483, see Cauchy development, 18 also strong cosmic censorship, weak cosmic Cauchy surface, 18 censorship, 618 causal dynamical triangulations, 565–567 cosmic microwave background, see CMB causal sets, 506 cosmic no-hair property of de Sitter spacetime, 533 causality violation, 17 cosmic shear, 171 CDT, see causal dynamical triangulations intrinsic alignment of galaxies, 129 CGRO, 148, 150, 151 lensing of the CMB, 129 Chandrasekhar mass, 387 probing dark energy, 129 characteristic code, 365 shear correlation functions, 128, 129 characteristic formulation, 366, 391 shear peaks, 129 characteristic initial data set, 455 cosmological constant, 11, 165, 166, 180, 555, 563, characteristic initial value problem, 454 577, 582, 583, 587, 600–602

Index 669

cosmological principle, 480 energy conditions, 18 critical phenomena, 370 energy-momentum tensor, 453 Cronstrom¨ condition, 492 conservation, 11 CSS, see continuously self-similar entanglement entropy, 658 curvature, 11 EOB, see effective-one-body Cyg X-1, 134, 139, 237 EOS, see equation of state Cygnus A, 134, 142 equation of motion, 303 cylindrical gravitational wave spacetimes, 364 equation of state, 375, 382 equivalence principle, see weak equivalence dark energy, 8–9, 166–167, 171 principle, strong equivalence principle, Einstein alternatives, 226 equivalence principle equation-of-state, 129 ergo region, 29, 471 dark matter, 8, 10, 118, 122–125, 128, 130, 165 Euclid space mission, 129 bullet clusters, 128 Euler equation (relativistic), 102 cold, 166 event horizon, 17, 28, 133, 142, 469 microlensing by compact objects (MACHOs), 125 exact solutions, 5, 10, 16 de Sitter, 3 excision, 365, 367 deflection of light, 70–72 existence theorems, 10, 11, 18 density parameters, 165, 206 exoplanets, 4 dimensional reduction, 509 extremal Kerr, 471 DIRE, see direct integration of relaxed Einstein extreme-mass-ratio inspiral (EMRI), 300, 302, 304, equation 309, 313, 322 direct integration of relaxed Einstein equation, 296, 299, 322 f (R) theories, 67, 167 discretely self-similar, 371 f-modes, 386 DOC, see domain of outer communication Fermi satellite, 157 domain of outer communication, 441, 469 finite difference method, 368 dominant energy condition, 414 finite volume methods, 369 double null foliation, 455 firewall, 400 double pulsar, 4–6, 81 fitting problem, 228 drag-free, 246, 269, 282 flatness problem, 178–179 DSS, see discretely self-similar FLRW models, 4, 10, 18, 30–33, 163–165, 401, 480 perturbations, 34–35, 167–169, 200 E-mode polarization, 7, 211, 212 curvature, 184 EAA, see effective average action tensor, 169, 184, 186, 215 Eddington, 3 velocity, 226 Eddington limit, 135 frame-dragging, 390 Eddington luminosity, 138, 156 frequency–mass diagram, 310 EEP, see Einstein equivalence principle Friedmann equation, 164, 165, 176 effective average action, 556–568 Friedmann–Lemaˆıtre–Robertson–Walker spacetimes, effective field theory, 298, 299, 322, 504, 554, 599, see FLRW models 600 Fuchsian PDE analysis, 451 effective-one-body, 290, 304, 305, 308, 309, 315, 316, functional renormalization group FRG, 556–561 322, 378 fuzzballs, 655 EFT, see effective field theory Einstein equations, 11, 164, 203, 476 Galactic center Einstein equivalence principle, 51, 56, 59–61, 67 stellar orbits, 136 Einstein flow, 480 Galactic microlensing surveys, 118, 125 Einstein metrics, 486 extrasolar planets, 126 Einstein static model, 162 galaxy surveys, 170–173, 195 Einstein Telescope, 245, 264, 281, 289 galaxy–black hole correlation, 137 Einstein–Maxwell theory, 453 galaxy–galaxy lensing, 130 Einstein-perfect fluid theory, 453 gamma-ray bursts, see GRBs Einstein-scalar field theory, 453 gauge dependence, 168 element formation, 5 generalized harmonic coordinates, 367 eLISA, 246, 267, 268, 271 generating techniques, 5 elliptic–hyperbolic system, 489 GEO 600, 243, 247, 248, 251, 252, 255, 262, 281

670 Index

geodesic, 14 GeV emission, 157 geodesic deviation, 14–15 long, 148, 149, 153, 154, 157, 158 geodesic equation, 200, 225 other types, 155 geodesic incompleteness, 19 redshifts, 157 geodesic self-force problem, 378 shocks, 150 geometrization, 441 external, 151, 159 geometrodynamics, 502, 568, 572, 575, 576, 585 internal, 151, 159 global hyperbolicity, 18 short, 148, 149, 153–155, 157, 158, 382 Global Positioning System, 4, 58, 80 spectra, 157 Gowdy spacetimes, 451, 490 X-ray flashes, 152 GPS, see Global Positioning System, 10 Gregory–Laflamme instability, 394, 616 graceful exit, 180 group field theory, 580, 584, 602, 606 Grand Challenge, 365 GSF, see gravitational self-force formalism graph manifold, 482 gravitational collapse, 10, 26, 369 Hadamard/Friedlander formulas, 492 gravitational lensing, 4, 8, 10, 37–40, 118, 199, 228 Hamiltonian reduction, 484 convergence and shear, 120, 121 harmonic asymptotics, 422 critical curves and caustics, 121, 123, 124 harmonic coordinates, 366 critical surface mass density, 120 harmonic gauge, 457, 468 deflection potential, 120 Hawking effect, 533 Einstein radius, 122 Hawking mass, 430 Einstein ring, 118, 121, 122 Hawking radiation, 169 Fermat potential, 123 hesitation dynamics, 225 magnification, 121, 123–127 hidden symmetries, 510 mass profiles of deflectors, 119, 121, 123 higher-dimensional gravity, 614–625 mass-sheet degeneracy, 123 HMNS, see hyper-massive neutron star multiple images, 118, 121 Horava–Lifshitzˇ gravity, 506 natural telescopes, 131 holography, 395 of the CMB, 206, 214, 230 holonomies, 570, 572, 574 time delay and Hubble constant, 123 hoop conjecture, 364, 389, 391 weak vs. strong lensing, 120, 127 horizon problem, 176–178 gravitational radiation, 12, 14, 41, 83–91 horizons gravitational redshift, 4, 52, 56–58, 82 cosmological, 17 gravitational self-force formalism, 291, 300, 302–304, event, see event horizons 310, 316, 322 hot spot, 210, 211, 225 gravitational wave detection results, 248, 318, Hubble constant, 5, 123, 164, 206 327–329, 332, 333 Huygens’ principle, 492 gravitational wave extraction, 367 hyper-massive neutron star (HMNS), 384 gravitational waveform, 276, 290, 291, 296, 297, 299, hyperbolizable, 483 301, 304, 305, 308–310, 315–319, 321, 323, 325, hyperbolizable manifold, 487 330 hyperboloidal formulation, 366, 368 gravitational waves, 5, 10, 40–44, 155, 158, 476 hypermassive neutron star, 383 cylindrical, 41 hypernovae, 149 detection, see Chapter 5, 42 emission, see Chapter 6, 42 immersed MOTS, 440 plane, 41 impulsive gravitational waves, 475 primordial, 216, 227 incompressible torus, 482 weak, 40 inflation, 17, 33–34, 43, 169, see Section 4.2, 179, 659 gravitomagnetism, 78 alternatives, 222 graviton mass, 70, 91 chaotic, 181 Gravity Probe B (GPB), 78 in Bianchi models, 225 gravity–hydrodynamics duality, 397 in inhomogeneous models, 226 gravity-gradient (Newtonian) noise, 245, 251, 264, new, 181 265, 268, 281 old, 179–181 GRBs, 148, 318, 320, 324, 326–329 slow-roll, 181–184 afterglow, 148, 151–153, 157 inflaton, 8, 35, 181, 222, 226 counterparts, 148 information loss paradox, 539

Index 671

inhomogeneous geometries, 167 LQC, see loop quantum gravity, loop quantum initial data set, 412, 453 cosmology initial value problem, 18 LQG, see loop quantum gravity innermost stable circular orbit, see ISCO luminous arcs, 118, 128, 131 interacting quantum fields, 546 abundance and arc statistics, 128 intergalactic medium chemical composition, 154 magnetic reconnection, 151 intermediate-mass black hole binaries, 292, 304, 313, mass determination with gravitational lensing, 122 318 mass substructure in gravitational lenses, 123 inverse Compton effect, 150, 158 mass-sheet degeneracy, 123 inverse mean curvature flow , 431 Massive Astrophysical Compact Halo Objects irrational exuberance, 511 (MACHOs), 125, 126 ISCO, 29, 381 massive gravity, 167 isolated black holes, 324 matched filtering template, 315–318, 321–323, 332, isolated neutron stars, 328 333 maximal Cauchy development, 458 Jang’s equation, 424, 437 maximal data, 418 jet, 142–144, 151, 152, 156, 157, 159 maximal slicing, 363 opening angle, 152, 153, 155 method of lines, 369 junction conditions, 16 metric, 11, 12 metric theory of gravity, 51, 52, 56, 59–63, 65, 71, 74, K(π,1) manifolds, 481 75, 87, 89 MHD simulations, 142 KAGRA, 251, 264, 281 microlensing, 4, 118, 135 Kahn–Penrose solution, 477 microlocal spectrum condition, 550 Kaluza–Klein bubbles, 618 Minkowski space Kaluza–Klein theory, 615–616 compactification, 17 Kantowski–Sachs spacetimes, 224 MiSaTaQuWa equation, 303 Kasner spacetimes, 398, 450, 451 Misner wormhole initial data, 362 Kerr, 437 mixmaster, 398 Kerr solution, 10, 22, 25, 470 Mixmaster behavior, 450 Killing vector, 14 modified gravity, 171, 222 Kottler solution, 22, 25 MOND, 166 Kruskal diagram, 24 Morawetz vector fields, 466 Mostow rigidity theorem, 486 2 L bounded curvature conjecture, 462 MOTS stability inequality, 436 lapse function, 425 MOTS stability operator, 436 Large Hadron Collider, 166, 389 MOTS: marginally outer trapped surface, 433 laser interferometry, 243, 247, 267 moving puncture method, 367 last scattering surface multipolar post-Minkowskian–post-Newtonian initial data, 202 formalism (MPM), 294, 295 Lemaˆıtre–Tolman–Bondi (LTB) models, 223 multiverse, 224 lensing potential, 208 Myers–Perry black holes, 438, 619 LHC, see Large Hadron Collider light-bending, 3, 4 N-body simulations, 171 light-cone estimates, 490, 492 naked singularities, 364, 371 LIGO, 247, 249 near-CMC, 416 LIGO India, 281 near-zone post-Newtonian approximation, 295 LIGO/VIRGO/KAGRA, 384 neutrinos LISA, 246, 265, 267, 269, 271, 282 high energy, 158 LISA Pathfinder (LPF), 246, 265, 270, 271, 282 number of species, 5 Liu–Yau mass, 427 neutron star loop quantum gravity, 504–510 viscosity, 110 Hamiltonian theory, 567–577 neutron star equation of state (EoS), 312, 314, 320, loop quantum cosmology, 585–592 321, 323, 326, 329, 330 spin foams, 504–509, 577–584 neutron stars, 100, 134, 149, 154, 382, 501 Lorentz cone spacetimes, 486 maximum mass, 102

672 Index

minimum mass, 105 pulsar timing array, 272, 288, 289, 310, 324, 332–334 minimum period, 102 puncture initial data, 364 radius, 103, 105 redshift, 103 QCD, 554, 568, 573, 577, 581, 583, 584, 591, 595, Newtonian approximation, 156 605 in cosmology, 171–172 QED, 568, 573, 577, 583, 584, 591, 604, 605 NGC 4258, 137 QEG quantum Einstein gravity, 562–564, 584, 604 No-Hair theorem, 144–145 QSOs, see quasars non-Gaussianity, 171, 172, 187–189, 193 quadrupole formula, 289, 290, 293, 297, 364 nonlinear σ models, 377 quanta of geometry, 554, 574, 577, 604, 606 Nordtvedt effect, 75 quantum black holes, 592–597, 602, 655 NR, see numerical relativity quantum bounce, 586, 587, 589–591, 604, 605 null condition, 469 quantum Einstein gravity, see QEG null constraint equations, 455 quantum field theory, 167 null forms, 464 quantum field theory in curved spacetime, 169, 503, numerical relativity, 10, see Chapter 7, 288, 290, 291, 513 299, 304, 305, 308, 309, 315, 316, 321 quantum horizons, 592–597 numerical simulations, 29, 156 quantum Riemannian geometry, 555, 570–575 quark confinement, 655 optical depth, 198, 206, 208 quark–gluon plasma (QGP), 395 optical structure equations, 456, 466 quasars, 5, 135 orthonormal frame formalism, 491 quasi-local mass, 424 oscillons, 374 quasi-normal mode spectrum of Kerr, 378 quasi-normal modes, 388 parametrix, 457 parametrized post-Newtonian formalism, 6, 61–63, R-parity, 166 65–67, 75, 77, 90 r-process, 385 Penrose diagram, 17 radiation pressure noise, 245, 250, 252–254, 263, 269 collapsing fluid spheres, 26 radiation reaction, 291, 297, 298, 302, 305, 307, 309, Schwarzschild solution, 24 322 Penrose process, 142 radio astronomy, 5 perihelion shift, 4, 73, 74 Randall–Sundrum models, 394 perturbation theory, 291, 300, 305 Raychaudhuri equation, 454 perturbations recoil velocity, 379, 380 in inflation, 184–187 redshift effect, 470 perturbative quantum gravity, 502, 633–636 reduced Hamiltonian, 485 Petrov classification, 5, 16 Regge calculus, 506, 566, 574, 578, 580–583, 600, photoelectric effect, 3, 6 602 photon counting (shot) noise, 246, 247, 250–252, 254, reheating, 169, 183 256, 258, 262, 268 reionization, 206 Planck satellite, 163, 206 Reissner–Nordstrom¨ solution, 22, 25 plane-symmetric gravitational wave collisions, relativistic aberration, 199 389 relativistic heavy ion collisions, 389, 391, 397, 656 Poincare´ Conjecture, 481 relativistic stars, 100 POLARBEAR, 7, 211, 215 stability, 106 positive energy theorem, 418 resonant-bar (acoustical) detectors, 243 positive mass theorem, 424, 442 RG flow, 556, 560, 561, 652 post-Newtonian (PN) formalism, 290–292, 294–299, RHIC, see relativistic heavy ion collisions 301, 304–306, 309, 315–317 Ricci identities, 11 post-Newtonian expansions, 378 Ricci scalar, 11 PPN, see parametrized post-Newtonian formalism Ricci tensor, 11, 15 precision cosmology, 7, 35, 164, 195–219, 228 Riemann moduli space, 484 preheating, 183 Riemannian Penrose Inequality, 431 pseudo-spectral method, 368 Rossby waves, 108 PSR1913+16, 242 PTA, see pulsar timing array Sachs–Wolfe effect, 201, 202, 211 pulsar, 4, 5 integrated, 171, 201, 204

Index 673

Sagittarius A, 135, see also Galactic Center, 145 supermassive black hole mergers, 380 scalar field, 34, 167, 169, 180 supernovae, 153, 154, 166, 288, 312, 319, 324, 325, scalar–tensor theories, 61, 64, 65, 89 327–330 scaling laws, 371 superradiance, 471 Schwarzschild, 3 supersymmetry, 165, 167, 502–508, 625–627 Schwarzschild solution, 10, 20–22, 25, 469 extended supersymmetry, 626 maximal extension, 22–25 local supersymmetry, 627 Schwarzschild–Tangherlini black hole, 393, 614 surface Hamiltonian, 425 SDSS, 170, 195 Swift, 149, 153, 155, 156, 158 Seifert fibered space, 482 Swiss cheese models, 228–230 seismic noise, 245, 250, 259 symmetry groups, 5, 14 self-similar space times, 227, 486 synchrotron emission, 150 SEP, see strong equivalence principle Szekeres solution, 477 SGO-mid, 265–267, 271 shift vector, 425 TAMA, 247–249 short-pulse method, 474 Teichmüller space, 484 simplicial decomposition, 566, 571, 574, 575, 606 tensor calculus, 11 singularity tensor spectral index, 187 cosmological, 225, 226, 398 tensor–vector–scalar theories (TeVeS), 69, 166 singularity resolution in LQG, 585–588 tetrads, 12, 13 singularity theorems, 10, 11, 15, 18–19, 433, 450 null, 13 Sloan Digital Sky Survey, see SDSS orthonormal, 13 slow-roll parameter, 182 thermal noise, 245, 247, 250, 252, 253, 262–264, solitons, 390 281 South Pole Telescope, see SPT thermal states, 526 space-time harmonic gauge, 489 Thurston conjecture, 483 spacetime invariants, 5 tidal capture, 156 spatial gauge, 485 of stars, 155 spatial harmonic gauge, 489 tidal radius, 156, 384 spectral tilt, 169, 206 tight-coupling approximation, 203 spherical space forms, 481 time delay of light, 72, 73, 82, 85 spikes, 398, 451 time of arrival (TOA), 273, 277 spin network, 593 time ordered products, 544 spin–orbit precession, 385 time-delay interferometry, 268 SPT, 163, 195, 206, 211, 215 time-symmetric initial data, 419 Sputnik, 5 topological censorship, 440, 442 Square Kilometer Array, 130 topological defects, 163 squeezed vacuum, 252, 262, 263 topology, 17 stability, 106 transverse-traceless tensor, 485 f -modes, 107 trapped surface, 389, 434, 473, 474 CFS instability, 107 trapping effect, 471 thermodynamic, 114 trumpet slice, 367 turning-point instability, 113 turning-point instability, 113 stability of Minkowski space-time, 466 twistor methods, 506 star formation, 153, 154 Type I critical solutions, 370 stellar-mass binaries, 288, 312 Type II critical solutions, 370 stochastic background, 288, 331–334 Stokes parameters, 211 U(1)-symmetric vacuum metrics, 451, 489 string theory uniqueness theorems, 10, 11, 18 non-perturbative aspects, 641–647 universal profile of dark matter halos, 128 perturbative aspects, 636–641 universality, 370 strong cosmic censorship, 450, 451, 462, 472 Universality of Free Fall (UFF), 51 strong equivalence principle, 61, 67, 74, 76, 77, 84, 87 Unruh effect, 528 structure formation, 30 UV and IR fixed points, 561–567, 601, 603 supergravity, 502–510, 627–636 supermassive black hole binaries, 244, 288, 311, 313, vacuum energy, 166 320, 324, 333 variation of G,77

674 Index

Vassiliev higher spin theories, 506 Weyl tensor, 15 vector–tensor theories, 68 Wick rotation, 566, 570 Virgo, 247, 249 Wilson loops, 652 Virgo cluster WMAP, 163, 199, 206, 585, 588, 589 infall, 199 vorticity, 224 X-ray binary, 138 X-ray sources, 134 Wang–Yau quasi-local energy, 428, 429 persistent, 138 wave equation, 476 transient, 138 wave front set of distribution, 547 wave map, 377, 490 y-type distortion (of CMB spectrum), 196 wave-zone multipolar post-Minkowskian Yamabe invariant, 486 approximation, 294 Yamabe types: negative, zero, positive, weak cosmic censorship, 462, 472 483 weak equivalence principle, 51–53, 61, 76 Yamabe’s theorem, 484 weak gravitational lensing, 118, 126, 127, 171 Yang–Mills equations, 461, 463, 490, 492, bullet clusters, 128 494 weak null condition, 469 York formalism, 364 well-posedness, 457 WEP, see weak equivalence principle zoom-whirl orbital dynamics, 382