Назад
Index 621
scaled
limit, 265
metric, 268
scattering matrix, 495, 500–503, 505–506,
508–509
Schiff effect, 34, 41
Schott term, 248, 367–369, 373–374, 376–377,
379, 387, 391–392
Schwarzschild
black hole, 181, 265, 284, 290, 297, 327,
352, 357, 361, 405, 408, 422
coordinates, 147, 179, 190–191, 335, 408,
420–421, 519, 521
deformed, 188
geometry, see geometry
metric, 34–35, 179, 184, 188, 190, 220,
265, 288, 290, 296, 298, 303, 386,
419–420, 422, 483
singularity, 179–180, 185
solution, 485, 570
spacetime, 111, 119, 178, 190, 236, 290,
328, 333
Schwarzschild-de Sitter
metric, 264
solution, 35
Schwarzschild-Droste (SD), 569–571, 573–
576, 588, 595, see Schwarzschild
black hole, 561
metric, 569
second order, 49, 55–56, 129, 268–269,
283–285, 292, 298, 348, 388, 395,
397, 408, 410–412, 433, 551, 574,
581, 588–589, 593
corrections, 410
deviation, 588
Einstein tensor, 269
secular, 44, 126, 270, 412, 524, 562, 584
self-acceleration, 50–52, 410, 566
self-adjoint, 258, 260, 512
wave equation, 260
self-consistent, 227, 254, 261, 263, 270,
296, 396, 499, 502, 509, 561–562,
592–596
approach, 561–562, 593
equations, 269
method, 296, 596
perturbation, 263, 270
perturbative equation, 263, 270
radial fall prescription, 592–596
self-coupling, 7, 10–11, 19–20
self-field, 127–128, 150–151, 158, 269, 309,
415, 417, 426
divergent, 415, 417, 426
regularization, 128, 150–151, 158
self-force (SF), 259, 264, 270, 273–275, 277,
280–282, 285, 291–295, 297–305,
309–313, 316, 321–324, 327, 344,
356, 378, 395, 397–398, 401–404,
407–408, 410–413, 415–416, 440,
453, 532, 561–563, 582–586,
590–597
adiabatic, 412
post-adiabatic, 408
corrections, 253, 259, 261
effect, 253, 255, 261, 263, 269, 275–277,
294–295, 298, 300, 306, 412–413
gravitational, 263, 298, 306
electromagnetic, see electromagnetic
first-order, 411–412
gravitational, see gravitational
Newtonian, 273, 275, 297, 564, 584
problem, 255, 273, 282, 285, 291, 300,
310, 325
Regge-Wheeler, 346
term, 261, 594
self-interaction, 6, 9, 151, 383, 468, 552
semi-latus rectum, 352, 355, 593
series
Hadamard, 257–258
nonlinear, 140
perturbation, 11
post-Minkowskian, 142, 168
post-Newtonian, see post-Newtonian
formal, 132, 142
Taylor, 227, 266
finite, 266
SF (self-force), see self-force
shell, 174–175, 254, 321–322, 334, 350–351,
372, 536
matter, 254
radius, 321
short distance, 256, 534, 558
SI (Syst`eme International ), 67–71, 74, 77–81,
83–84
silicon, 79, 81–82, 84
XRCD, see XRCD
singular
behavior, 155, 256–257, 259, 349, 583, 586
coefficient, 151, 155
field, 271, 280, 282, 299, 302, 305,
318–321, 323–324, 331, 339, 358,
403, 419
limit, 152
piece, 323, 333, 405
skeleton Hamiltonian, 177–178
small
acceleration, 26, 48, 53–54, 272, 289
body, 253, 261, 270, 408, 593, 596
622 Index
mass, 3, 13, 20, 37, 160, 271–272, 276,
283, 292–293, 300, 302, 328, 347,
418, 432, 443, 563, 582, 590
object, 273–275, 279, 282–283, 289
smooth
function, 132, 256–266, 330, 338, 340,
359, 544
vector field, 256
solution
Brill-Lindquist, 175–176
distributional, 254, 256
Kerr geometry, 35
Misner-Lindquist, 175
numerical, see numerical
Schwarzschild, 485, 570
Schwarzschild-de Sitter, 35
unique, 131, 220, 257
vacuum, see vacuum
wave equation, see wave equation
source
charge-current, 254, 266
distributional, 254
effective, see effective source
EMRI, 396
matter, see matter
moments, 142–143, 145, 147–148
point particle, 255, 258, 264
post-Newtonian, 135–139
term, 129, 133, 138, 140, 154, 181, 198,
233, 253, 348–349, 351, 353,
397–398, 400, 408, 423, 575–576,
579, 596
space-like
hypersurface, see hypersurface
slice, 184, 253
spacetime
asymptotically flat, see asymptotically flat
spacetime
background, see background
curvature, 31, 310, 562
domain, 87, 92, 108–109
Finsler, 58–59
geometry, see geometry
globally hyperbolic, 113, 318
Kerr, see Kerr geometry
Minkowski, see Minkowski spacetime
Riemannian, 28, 58
Schwarzschild, see Schwarzschild
stationary, 94, 369
special relativity, 28, 44, 87, 103, 297,
463–464, 467
speed of light, 2, 28–30, 44, 69, 126, 167, 416,
570, see photon speed
spherical harmonics, 144–145, 161, 286, 294,
336–338, 350–351, 353, 355–358,
405, 576, 586
spin
coupling
Papapetrou equation, 148
spin-orbit, 162, 196–197
spin-spin, 127
to curvature, 148, 162
force, 261, 263, 269
precession, 163, 193, 199
spin-2, 18, 128, 294, 462, 469, 471, 479
spinning particle, 31, 128, 148, 162
supplementary condition, 149
spin-foam model, 537, 541–543
spin-networks, 536, 542, 558
spontaneous emission, 492
Standard Model, 1–5, 7–11, 15–17, 20–22,
464
extensions, 21
state of the art, 128, 333, 361, 561, 565, 590,
592
beyond, 593
stationary spacetime, 94, 369
step (Heaviside step function)
discontinuity, 360
distribution, 581, 589
function, 241, 317–318, 496
STF, 134, 139, 141, 144–145, 204, 286–287,
361, see symmetric-trace-free
tensor, 145, 286
Stone-von Neumann theorem, 539
stress-energy tensor, 93, 129, 131, 147–148,
150–151, 171, 181, 183–184, 200,
253–255, 277, 283–285, 287–288,
291, 398, 405, 423–424, 576, 583,
see pseudo-tensor
conservation, 583
stress-energy-momentum, 109
string theory, 26, 45, 462, 463
strong
equivalence principle, 41, 49, 76, 471, 475,
479, 565
interaction, 2, 4, 12, 15–16, 22
nuclear interactions, 1
Strong-Field Predictions, 471
sufficiently small
body, 253, 261
neighborhood, 257, 258
superstring theories, 21
supersymmetry, 21, 22, 47, 462, 480
supplementary phase, 230
symmetric mass ratio, 157, 213, 217, 223, 431,
432
Index 623
symmetric-trace-free (STF), 134, see STF
symmetry group, 3, 4–6, 20–21, 106, 195,
537–539, 544
T
T-parity, 371, 386
tail, 138–139, 146, 209, 259, 330–332, 387,
390, 428, 436, 561, 584–586
component, 586
contribution, 329, 332, 378, 428
effect, 161, 168, 214, 230, 232, 428
factor, 230, 232–233, 237
field, 330
function, 382, 386
Green’s, 401
GW, see gravitational wave
integral, 146, 161, 429
part, 378, 401, 403, 584
ringing, 213
term, 203, 205, 240, 317, 334, 369, 379,
382–384, 386, 388, 392, 428
Taylor
approximants, 227, 236
T4, 215
coefficients, 228
expand, 138, 267, 285
expansion, 126, 221, 225–227, 237, 286,
312, 317, 373, 581, 587
series, 227, 266
finite, 266
Taylor-expanded, 212–213, 225, 228, 233, 235
templates, 127, 162, 396, 416, 453–455
adiabatic, 408
gravitational wave (GW), 125, 128, 156,
162, 164, 188, 211, 249, 396
inspiral, 125, 328
LISA, 597
post-Newtonian (PN), 416
theoretical, 127, 328, 396
waveforms, 211
tensor
anisotropic mass, 30
Einstein, see Einstein
second order, 269
energy-momentum, see energy-momentum
tensor
canonical, 91
stress, 109
Levi-Civita, 274, 286
quadrupole, 192, 198, 205
mass-quadrupole, 192, 205
Riemann, see Riemann
STF, 145, 286
stress-energy, see stress-energy tensor
Weyl, 398, 477, 478
test-particle limit, 191, 221
Testing Basic Laws of Gravitation, 25–60
New Effects, 45
tetrad, 91, 313–314, 339, 398, 537
Teukolsky equation, 346, 348, 396–400, 403
TeVeS (Tensor-Vector-Scalar) model, 483
theoretical templates, 127, 328, 396
Thorne-Hartle-Zhang (THZ) coordinates, 313,
see THZ
three-dimensional gravity, 534–535, 544
transplanckian region, 563
Trautman-Bondi-Sachs, 105
THZ, 283, 287–288, 299, 313, see Thorne-
Hartle-Zhang
tidal
acceleration, 289–290
deformation, 367, 391
distortion, 271–272, 288, 305, 420
effects, 274, 289, 449, 463
forces, 449, 478, 565
properties of neutron stars, 249
tides, 289
time
dependence, 26, 39, 53, 103, 290, 413, 473
domain, 87, 92, 108–109, 302–303, 327,
333–334, 343, 347–350, 356, 375,
395, 400, 496, 498, 509, 517, 578
interval, 270
scale, 51, 126, 274, 283, 287, 289–290,
395–396, 398, 453, 510, 526, 562,
590, 596
time-dependent gravitational constant, 44
time-like
hypersurface, 98, 254
surface, 255
two-body problem, 125–164, 211–249, 273,
275, 395, 562, 578, 582
U
UFF, 30–31, 41–42, 46, 50, 57, see universality
of free fall
unbarred
coordinates, 266
metric, 266
uncertainty principle, 9
uniformity requirement, 265, 266
unique solution, 131, 220, 257
uniqueness of acceleration, 565–566, 568–569,
585
Units, 67–84
ampere, see ampere
624 Index
astronomical unit, 462
atomic units, 71, 73
base units, new definitions of, 83
candela, 68
geometrized units, 329
kelvin, 68, 75, 84
kilogram, see kilogram
meter, 68–69, 74
natural, 71, 73
Planck, 71, 73, 557
second, 67–69, 72, 75, 80, 84
universality of free fall (UFF), 30, 463, 464,
514, see UFF
V
vacuum
energy, 31, 491–492, 494, 506
field fluctuations, 491–492, 503, 508, 526
fluctuation, 492–494, 504, 510
solution, 35, 175, 265, 273, 278, 283, 286,
287, 291, 292, 346
state, 492, 497, 501–502, 507, 511
wave equation, 574
van der Waals force, 492
van Vleck-Morette determinant, 257
Virgo, 211, 416, 475
von Klitzing constant, 76
W
watt balance, 78–80, 82–84
wave equation
homogeneous, see homogeneous
inhomogeneous, 202, 403
linear, 256, 310, 316
scalar, 310
self-adjoint, 260
solution, 136, 138, 140, 317–319, 383
vacuum, 574
wave operator, 264, 283–284, 316, 353, 401,
579
waveform of compact binaries, 145
waveforms, 232, 237, 245–246, 399, 411–413,
433, 452–454, 578, 592
adiabatic, 395, 397–398, 412–413,
453–454
analytical, 212, 243
approximate, 453
EMRI, 327, 408, 455
EOB, 213, 223, 238–239, 243
gravitational (GW), see gravitational wave
inspiral, see inspiral
kludge, 453–455
multipolar, 236–237
numerical (NR), 213, 223, 235, 243, 396
polarization, 143–145, 160–161, 207
post-Newtonian, 147, 160
template, 211
wavefront set, 254
weak interaction, 2, 4–8, 11
weakly isolated horizon, 116, see WIH
well-posed initial value formulation, 270
Weyl
curvature, 517, 519
scalars, 298
tensor, 398, 477, 478
white dwarfs, 396, 449
WIH, 116–118, see weakly isolated horizon
symmetry, 117–118
wild oscillation, 264
Wilson loop, 533
window function, 281–282, 288, 303
Woolsthorpe apple tree, 561, 597
worldtube, 115, 264, 357, 477
auxiliary, 357
X
X-ray crystal density, 79, 81, see XRCD
XRCD, 79, 81–84
silicon, 79, 81–82, 84
Y
Yang-Mills
gauge field, 533, 536
theory, 533, 536, 538
Z
Zerilli, 240, 574, 577, see Regge-Wheeler-
Zerilli
equation, 298, 574–575, 581
potential, 591
zeroth order, 283
(zeta) function, see Riemann-Hurwitz
-function
zitterbewegung, 56