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Index
A
Abraham, 49, 270, 324, 504
Abraham-Lorentz
equation, 49
vector, 504
Abraham-Lorentz-Dirac equation, 270
acceleration
Pioneer, 48, 54
scale, 48, 54, 289, 480
self-acceleration, 50–52, 410, 566
small, see small acceleration
tidal, 289–290
uniqueness of, see uniqueness of
acceleration
action
Einstein-Hilbert, 90, 98, 128, 462, 468,
480, 533, 537, 543
Einstein-Infeld-Hoffmann (EIH), 467
Fokker, 461, 465–467, 469, 486
Holst, 537
matter, 90, 463–467, 485–486
Palatini, 537
variables, 217, 219
adiabatic, 368, see non-adiabatic,
post-adiabatic
approximation, 590, 597
inspiral, 120
kludge waveforms, 453–455
last stable orbit, 222
limit, 232, 235, 398
orbital evolution, 328
quasi-circular inspiral, see inspiral
self-force, 412
signals, 228
templates, 408
waveforms, see waveforms
adiabaticity, 562, 584, 590
ADM, see Arnowitt, Deser and Misner
4-momentum, 102–103
and Bondi masses, 115
and Bondi-Sachs energy-momentum, 122
and Komar Mass, 103
angular momentum, 104–105
approach, 184
canonical formalism, 173
coordinates, 159, 184–185
energy, 100–101, 103, 105, 107, 112, 182
Hamiltonian, 162, 174
mass, 102–104, 107–108, 110, 112–113,
119–120, 180, 428, 430
mass-energy, 180
momentum, 102
alternative theories of gravity, 461–462, 468
aquadratic kinetic terms, 481
Aquadratic Lagrangians, 481
diagrammatic representation, 465
extended bodies, 149, 477, 485
mass-dependent models, 481
metric coupling, 462–464
modified Newtonian dynamics, see MOND
nonminimal couplings, 486
scalar-tensor theories, see scalar-tensor
ampere, 67–68, 70, 75, 77, 84, 351
analytic
case, 257
continuation, 133, 138, 153, 155, 214, 235,
420, 423, 426
analytical waveforms, 212, 243
angle average, 259
angular average, 152, 156, 267
angular momentum, 35, 40, 87–90, 95, 97,
104, 108, 114–115, 121–122, 149,
231–233, 242, 369, 450, 511
ADM, 104–105
and energy, 33, 91–92, 94, 293, 418
Bondi-Sachs, 107
conservation, 18, 33
defined at spatial infinity, 97, 104–105
L. Blanchet, A. Spallicci, and B. Whiting (eds.), Mass and Motion in General Relativity, 605
Fundamental Theories of Physics 162, DOI 10.1007/978-90-481-3015-3,
c
Springer Science+Business Media B.V. 2011
606 Index
density, 231
flux, 227, 418
for the gravitational field, 91–94, 121
horizon, 116, 118
in general relativity, 87, 91, 121–122
intrinsic, 128
Komar, 95, 105, 114, 120
orbital, 164, 190, 219, 450
Quasi-Local, 114
spin, 148
anisotropic
mass tensor, 30
speed of light, 30, 44
anisotropy (effects), 30, 43, 57
anti-de Sitter, 99, 534
anti-hydrogen, 30, 32
antidamping, 367, 390, 392
approximation methods, 125–126, 169, 413
Aristotle (Aristot´el¯es), 563
Arnowitt, Deser and Misner (ADM), 97, 102,
158, 169, 216, see ADM
Ashtekar, 115, 533–534, 536–537, 540
formulation of gravity, 536
variables, 533–534, 537
Ashtekar-Barbero connection, 537
Ashtekar-Barbero variable, 537
Ashtekar-Lewandowski measure, 540
asphericity of the object, 272
assumption, unjustified, 264, 325
astronomical unit, 462
astronomy, 283, 367
astrophysical observations, 28, 34, 48, 128
asymptotic past, 259
asymptotically flat spacetime, 97, 106, 117,
120, 122, 195, 267
atomic mass, 73, 77–79, 81
auxiliary
metric, 129, 423
worldtube, 357
average
angle, 259
angular, 152, 156, 267
Avogadro constant, 70, 78–79, 81
axiomatic approach, 264, 311, 322–323, 328,
583
axioms
Detweiler-Whiting, 323
Quinn-Wald, 322
B
back reaction, 49, 403
back-action, 561–569, 590–591, 596
Newtonian, see Newtonian
background
cosmic microwave, 43, 45, 479
field, 387, 561, 574, 588, 589
geodesic, 561–562, 584–585, 593–594
geometry, see geometry
metric, 96, 263–264, 287–288, 295, 329,
352, 387–389, 402, 405, 409, 454,
464, 518, 543, 563, 569, 582,
584–585, 587–588, 594
motion, 581, 595
spacetime, 95, 255, 258, 267–268, 270,
295, 299, 310, 328, 331, 352, 582,
584, 593
Barbero connection, variable, 537
Barbero-Immirzi ambiguity, parameter, 537
barred
coordinates, 266
metric, 265–266
Bartnik mass, 113
base units, new definitions of, 83
Belinfante-Rosenfeld procedure, 91
Bianchi identities, 89, 184, 200, 369, 387, 514
Bianchi identity, 129, 255, 267, 283–284, 296,
387–388, 392
linearized, 255, 267
binary
black hole, 26, 37, 120, 125, 175, 177, 182,
196, 211, 214–215, 221–222, 246,
248–249, 395, 416–417, 476
coalescing, 211, 213, 248–249
neutron stars, 249, 253
pulsar, 126–128, 189, 473–475, 483
Hulse-Taylor, 126, 473–474
system, coalescing, 212
biscalar, 384, 385
black hole
coalescing binary, 211, 213, 248–249, see
binary
central, 396, 412, 448–453, 455–456, 582
charged, 51
geometry, 272, 304, 344, 453
in three-dimensional Lorentzian anti-de
Sitter gravity, 534
inspiral, 211–212, 215, 240, 249, 278, 305,
449–450
massive, 276, 327, 367, 443–445,
448–449, 561, 564, 582, 597
perturbation theory, 226, 343, 417, 433
perturbations, 344, 561, 574–575, 577
body, see two-body problem
effective one-body, see EOB
small body, see small body
sufficiently, 253, 261
two-body, see two-body problem
Index 607
Bondi
coordinates, 105
energy, 105, 107
mass, 107, 115
Bondi-Metzner-Sachs (BMS), 106
Bondi-Sachs
4-momentum, 106–107
angular momentum, 107
energy, 111–112
energy-momentum, 122
boundedness, 348
Boyer-Lindquist, 335, 338–339, 341–342, 358,
362, 397
angular coordinates, 362
components, 338–339, 342, 358
coordinates, 338–339, 341, 397
Schwarzschild coordinates, 335
Brill-Lindquist, 175–176, 178, 180, 185
black hole, 175, 185
solution, 175–176
Brown-York energy, 109–111, 114
Brownian motion, 492, 502
Burke-Thorne
coordinate condition, 192, 204
radiation-reaction force, 428
C
caesium, 68, 84
candela, 68
candidates for dark matter, 480
canonical
conjugate, 173
energy-momentum tensor, 91
form, 118, 167, 172–173, 194, 196
formalism, 167, 172–173, 194
general relativity, 171, 173, 537
moments, 145, 147
quantization, 533
transformation, 97, 99, 116–118, 188
variables, 537
Capra (meeting), 306, 392, 568, 583,
597
Carter constant, 293, 391, 398
Casimir
energy, 491, 494, 505–507, 526
force, 492, 494, 505–507
Cassini, 39, 469–470, 474–475, 522,
525
Cauchy
hypersurface, 113, 352
problem, 468, 482, 486, 536
surface, 352–353
causality, 323, 412, 482, 496, 499, 501
centre of mass, 13, 16, 20, 50–52, 149, 157,
160, 177–178, 187, 190, 195–197,
199, 208, 216–217, 220, 267, 270,
272–273, 275, 289, 324, 431, 477,
566–568
coordinates, 267
frame, 177–178, 187, 190, 217, 220
integral, 431
shift, 566, 568
challenges, 17, 68, 83, 119, 298, 331,
456–457
characteristics, 1, 8, 17–18, 294, 332,
345, 449–450, 456, 558
of the Higgs Boson, 8
charge conservation, 46, 52–53, 60
charge-current source, 254, 266
charged
black hole, 51
lepton, 17–18
particle, 3–4, 36, 49, 76, 277, 322
Chern-Simons theory, 544
Christoffel symbol (connection), 33, 57, 259,
285, 574, 582
circular orbit, 40, 58, 128, 160–161, 178,
190, 206–207, 215, 220–222,
224, 226–227, 231–232, 236, 275,
282, 297–298, 300–301, 303, 349,
354–355, 357, 401, 411–413, 415,
417–418, 421–422, 430–431, 450,
562, 566, 596
Clebsh-Gordan coefficients, intertwiners, 540
co-dimension two, 255
CODATA, 71, 74–75, 77–79, 82–83
commutation, 329, 511, 512
compact objects, 103, 125, 128, 147, 150, 157,
396, 418, 444, 448–449, 472, 582
composition, 27, 30, 42, 50, 253, 565
Compton frequency, 68, 78, 80, 84
conformal decomposition, 100, 115
confusion noise, 452, 454
conservation
energy, 498, 562, 564, 584, 592
equation, 129, 170, 368, 370, 375
law, 25–27, 49, 89, 141, 170, 369, 387,
398, 468
probability, 10, 52
stress-energy tensor, 583
conservative
dynamics, 168, 174, 189, 219, 418
effect, 271, 293, 328, 410, 412–413, 415,
436, 584
Hamiltonians, 187
part, 158, 168, 224, 243, 292–293, 298,
411, 418, 427–429
608 Index
conserved
current, 89–90
energy, 159, 163
quantity, 88–89, 94–97, 100, 102, 104, 107,
116, 118, 412, 498
constants
Avogadro, 70, 78–79, 81
cosmological, see cosmological constant
Euler, 160
Euler-Mascheroni, 427
Fermi, 7
fine-structure, see fine-structure constant
fundamental, see fundamental
gravitational, see gravitational
Josephson, 76
Planck, see Planck
Rydberg, 79
von Klitzing, 76
constraint equation, 174–177, 181, 193, 194,
253
conventional values, 77
coordinates
barred, 266
Bondi, 105
center of mass, 267
components, 265–266, 274
Eddington-Finkelstein, 353–354, 578
Fermi normal, 258, 267–268, 285, 309, 313
fixed, 265
harmonic, 129, 131, 139, 140, 142–143,
147, 158–159, 168, 180, 184, 201,
235, 283, 423
locally inertial, see locally inertial
Schwarzschild, see Schwarzschild
shift, 268
Thorne-Hartle-Zhang (THZ), 287, 313
transformation, 57, 153, 267, 286, 295,
342, 375, 409, 422, 585
unbarred, 266
Copernicus, 304
correction
finite size, 261
first-order, 410
higher order, 19, 14, 15, 261, 270, 410
leading order, 267, 269, 411
perturbative, 261, 263, 269, 584
second-order, 410
self-force, 253, 259, 261
correlation coefficient, 75, 78
cosmic microwave background, 43, 45, 479
cosmological constant, 35, 492–493, 538, 544,
558
Coulomb, 30, 217, 271, 288, 305, 336, 348,
368, 378
coupled system, 254, 369, 534
covariant
derivative, 4, 7, 33, 148, 201, 274, 296,
329, 385, 388, 409, 477–478
expressions, 313
curve, 10, 180, 221, 256, 265, 267, 399, 440,
475
cylindrical function, 539–540
D
d’Alembert equation, 423, 425
d’Alembertian
equation, 129–131, 134, 137
operator, 129, 136, 152, 352, 423
d-dimensional gravitational constant, 154, 423
dark energy, 43, 48, 462, 479, 493
dark matter, 20–21, 31, 42–44, 48, 461–462,
476, 479–480, 482, 486, 493
around the Earth, 44
candidates, 480
detection of particles, 42
data analysis, 41, 211, 453–457, 597
de Broglie-Compton frequency, 80, 84
de Donder gauge, 129, 583, 585, 593, 596
relaxation, 583, 593
de Sitter, 35, 126, 264–265, 534
debate, 74–75, 254, 304, 561–562, 564,
569–573, 581, 591, 596
decay properties, 254
decomposition
conformal, 100, 115
factorized, 232
multiplicative, 216, 227, 232, 241, 244
multipole, see multipole
deformed, 169, 182, 188, 224, 473, 478, 544,
546, 549, 551, 565
Delaunay Hamiltonian, 217–218
(delta) ı-function, 148, 151, 179, 183,
213–214, 253–256, 316–318, 336,
348–349, 368, 373, 376, 380,
383–385, 396–398, 400–401, 423,
see Dirac
detection of dark matter particles, 42
determinant, 4, 128, 201, 257, 352, 423, 462,
505
Detweiler-Whiting, 260, 261, 318, 321, 323,
401–403, 419
approach, 323, 583
Axiom, 323
Green’s function, 260
Observation, 323
Reformulation, 260
regular two-point function, 318
singular Green’s function, 318
Index 609
deuterium, 79
deviation
geodesic, see geodesic
vector field, 268–269
second order, 588
DeWitt and Brehme, 259, 311, 379, 583
DeWitt-Brehme, 305
DeWitt-Brehme-Hobbs result, 386
diagrammatic representation, 465
differential equation, 34, 129, 131, 206, 211,
254, 257–258, 350, 381, 408, 495,
574
ordinary, see ordinary differential equation
partial, 254
dimensional
analysis, 291, 478
regularization, 153–156, 169, 175, 177,
183–184, 196, 214, 415, 420–421,
423, 425–426, 430, 433
Dirac
coordinate condition, 184
delta (ı-distribution) function, 137, 148,
150, 154, 167, 169, 171, 175, 181,
183, 423, 575–576, 581, 589, see
(delta) ı-function
derivation, 368
equation, 28, 30, 46
gauge condition, 101
displacement, 56, 268, 279, 312, 331, 446,
498–499, 503, 506, 517, 587
dissipative force, 412, 501
distribution of matter, 88, 145
distributional
solution, 254, 256
source, 254
divergence, 128, 131–134, 136, 140, 152, 337,
348, 353, 373, 378–379, 381–384,
386–387, 389, 391, 402, 405–406,
425, 496, 499, 502, 509, 515–516,
534, 561, 575, 578, 583, 586, 590
free, 89, 107, 112, 114–115, 183–184,
371–372, 388, 390
divergence-less, 129
domain of dependence, 89, 258
Doppler
effect, 36, 40, 464, 473
measurement, 573
ranging, 522
residuals, 522
shift, 80, 276, 448, 522
signal, 523
term, 58
tracking, 493
Drinfeld (quantum) double, 535, 544
Droste, 126, 561, 569, 571–572
dynamical invariants, 191
E
eccentric orbit, 301, 333, 350–351, 354–355,
396–397
Eddington-Finkelstein coordinates, 353–354,
578
EEP, 32, 41, 52, 60, see Einstein equivalence
principle
effective one body (EOB), see EOB
formalism, 211
methods, 563, 597
effective source, 230, 233, 282, 292, 294,
303–304
EIH, see Einstein-Infeld-Hoffmann
einbein, 389–390
Einstein
aether, 486
equivalence principle (EEP), 462, 464, 485,
see EEP
field equations, 26, 98, 125, 128, 129, 132,
139, 151, 153–154, 168, 173, 181,
184, 200–201, 324, 423, 574
linearized, see linearized
relaxed, 184
frame, 469
tensor, 90–91, 129, 269, 283, 388
second-order, 269
Einstein-Hilbert
Lagrangian, 514
theory, 533
Einstein-Infeld-Hoffmann (EIH), 158
action, 467
surface integral, 158, 169, 214
Einstein-Rosen bridge, 179, 180
electric
and magnetic field, 55
charge, 2–4, 49, 51, 121, 279, 309, 413
constant, 70
current, 76
field, 36, 49, 51, 52, 536
parity, 269
electrodynamics, 70, 253, 322, 368, 377, 391
electromagnetic
Abraham-Lorentz equation, 49
Abraham-Lorentz vector, 504
case, 259, 270, 325, 382, 386
DeWitt and Brehme, 259, 311, 379, 583
DeWitt-Brehme, 305
DeWitt-Brehme-Hobbs result, 386
Lorentz-Dirac equation, 368, 373, 377, 391
610 Index
Lorentz-Dirac force, 380, 382–383
radiation reaction, 277, 279
self-force, 255, 272, 291, 334, 583
electromagnetism, 4–6, 51, 266, 270, 563
in Minkowski spacetime, 266
electron mass, 71, 79
electrostatics, 279
electroweak interactions, 5
elementary particles, 1–3, 8, 21, 53
elements
caesium, 68, 84
deuterium, 79
hydrogen, see hydrogen
krypton, 69
silicon, 79, 81–82, 84
elliptic regularity, 256
EMRI, 301, 327, 347, 355, 361, 395, 411–413,
416, 443, 449–450, 582, 593, 597,
see extreme mass ratio inspiral
and IMRI, 449–451, 456
detection of, 327, 396, 451–452, 454
observations, 456
Signal Characteristics, 452–454
waveforms, 327, 408, 455
energy flux, 105, 150, 157, 187, 206, 215,
226–230, 233, 236–238, 243–244,
246–248, 591, 597
energy in General Relativity, 91
absorbed by the black hole, 578, 592
Bondi energy, 105, 107
Bondi mass, 107, 115
energy-momentum conservation, 367, 392,
515
energy-momentum tensor, 33, 88–91, 103,
109–110, 352, 369, 371–2, 376,
389, 476, 482, 493–494, 498–499,
505, 508, 510, 512, 514–518, 575
ADM and Bondi-Sachs, 122
canonical, 91
general relativity, 88, 121
Landau-Lifshitz, 91, 201
entropy conservation law, 170
EOB (effective one body)
approach, 212–213, 215–216, 223, 238
dynamics, 224, 230, 238–242
plunge phase, 239
effective horizon, 221
Hamiltonian, 213, 224, 231
late-inspiral dynamics, 248
plunge signal, 213
method, 212, 216, 219, 224, 249, 597
metric, 225, 247
EOM, 408, see equation of motion
ephemeris (ephemerides), 43, 525
epicycles, 304
equation of motion, 11, 25, 28, 33–34, 46,
49–51, 54–57, 60, 126–128, 150,
153, 156–159, 162–163, 168,
170, 174–175, 177, 181, 184,
186, 192–193, 200–201, 213–214,
216, 224–225, 238–239, 241–242,
254, 259–260, 309, 316, 321–322,
324, 367–368, 370–372, 377, 379,
391–392, 408, 411, 420–421, 425,
431, 451, 453, 465, 510–511,
515–516, 518, 534, 536, 551, 555,
558, 582–583, 596
equivalence principle, 41, 49, 76, 389, 462,
464, 471, 475, 479, 485, 491, 493,
514–515, 526–527, 565–566
Einstein, see Einstein
strong, see strong
weak, 565
ESA (European Space Agency), 443
Euler-Lagrange equations, 55, 551
even-parity, 230–231, 233, 236, 238, 418,
574–575
exotic, 46, 427
expansion
Fourier, 359–360
Hadamard, see Hadamard
higher order, 593
Laurent, 133, 151, 155, 380, 420, 497
matched asymptotic, 135, 259, 264, 305,
324–325, 328, 332, 583
multipole, see multipole
post-Newtonian (PN), see post-Newtonian
(PN)
Taylor, see Taylor
extended bodies, 149, 477, 485
extensions of the Standard Model, 21
extra-dimensions, 378, see higher dimensions
extreme mass ratio
binaries, 416
inspiral, 253, 416, 449, see EMRI
limit, 253, 432
extreme situations, 26, 27
extrinsic curvature, 93–94, 97–98, 100, 105,
109–110, 112, 114, 173, 184, 254
F
factorized decomposition, 232
false alarm rate, 456
far zone, 168, 186, 202, 205–206, 259, 267
Fermi normal coordinates, 258, 267–268, 285,
309, 313
Feynman propagator, 257