Einstein — Yang — Mills equations in spin coefficient formalism 27—28
Energy see also "Stress-energy tensor"
Energy condition and Higgs mechanism 149
Energy condition and microwave background 148
Energy condition on the stress-energy tensor 133
Energy condition, strong 148
Energy condition, strong, on the average 149
Energy, Bondi 17 76
Energy, extraction from ergoregion 144
Energy, Newman — Unti 76
Energy, radiation of in collapse 382 385—388
Energy-momentum tensor see "Stress-energy tensor"
Energy-momentum, heavenly 84
Energy-momentum, Ludvigsen conservation of 84
Enthalpy function, relativistic 368
Entropy and thermal equilibrium 509
Entropy in paraelectromagnetic dipole gas 519
Entropy, change in a virtual displacement 509
Entropy, density 504
Entropy, flux 494 497 498 514
Entropy, per baryon 341
Entropy, production 505—506
Entropy, singularity and increase of 142
Equation of state 361 364
Equation of state and weak cosmic censorship 177—181
Equation of state at equilibrium 499
Equilibrium 515—516
Equilibrium, equation of state 499
Equilibrium, function 515
Equilibrium, thermal, characterized 509—510
Ergoregion (sphere) 85 86 384
Ergoregion (sphere) and extraction of energy 144
Ergoregion (sphere) in Kerr metric 91 143 380
Ernst potential 259
Ether see "Universal rest frame"
Euler equation 87 92
Euler equation, relativistic form 366
Event horizon see "Horizon"
Extendibility of a space-time 155—156
Extendibility of a space-time, local 159
Exterior derivative, covariant 245
Exterior derivative, covariant, on bundle of orthonormal frames 248
Fourier's law 493 494
Fourier's law, relativistic 495
Friedmann model 101 149 330 335 336 371 427
Friedmann model and trapped surface 182—185
Friedmann model, singularity in 104
Future distinguishing conditions 119
G orbits 248—249
G structure 244 247
G structure, invariants of 250
g-boundary (geodesic) 140 152
g-boundary (geodesic) of  121
Galaxies, "seeding" of, by black holes 355
Galaxies, distribution of 342—345
Galaxies, radio 331
Galaxies, red shifts of 347
Galaxies, superclusters 345
Gauss equation, null analog 265
Gauss — Bonnet formula 128
Geodesic and shear-free congruence 21 217 227 228
Geodesic boundary see "Boundary"
Geodesic completeness 139
Geodesic curvature 264
Geodesic deviation and mass of an isolated system 55
Geodesic deviation, equation of 115
Geodesic deviation, modified 436—437
Geroch version of ADM 62
GHP (Geroch — Held — Penrose) formalism 213
Gibb's relation 495 499
Gibb's relation, covariant 501 516
Global hyperbolicity 121
Global hyperbolicity, stability of 175
Goldberg — Kerr gauge invariant radiation calculation 84
Goldberg — Sachs theorem 21 228
Goldberg — Sachs theorem, complex 249 265 267
Good cut equation 22 242 325
grand canonical ensemble 509
Grassman manifold, complex 222 230
Grassman representation of lines in  287
Gravitation, alternative theories of 488
Gravitational antenna and Brownian motion 404
Gravitational antenna and thermal vibration 405
Gravitational antenna of elastic solid 441—442
Gravitational antenna of free mass 442—443
Gravitational antenna, damping time of 439
Gravitational antenna, directivity pattern 446—447
Gravitational antenna, effective temperature of 451
Gravitational antenna, instrumentation of 443 446
Gravitational antenna, instrumentation of, with piezoelectric crystal 444
Gravitational antenna, laser interferometer 443
Gravitational antenna, low temperature 461
Gravitational antenna, mass quadrupole 437—441
Gravitational antenna, radiation resistance 439
Gravitational antenna, sensitivity of 447—448
Gravitational binding energy 470
Gravitational collapse and the formation of black holes 360—365 see
Gravitational constant, time variation of 483—485
Gravitational instability 345—347
Gravitational waves and polarization 398 417
Gravitational waves, absorption cross section 439
Gravitational waves, characteristic value, of amplitude 397
Gravitational waves, detection of 402—416
Gravitational waves, detection of, electromagnetically 409—413
Gravitational waves, detection of, with mechanical oscillator 403—406
Gravitational waves, detection of, with rotating two-body system 413—416
Gravitational waves, dispersion of 418 419 422 424 425 426 429
Gravitational waves, diurnal effects 454
Gravitational waves, identification of 455—460
Gravitational waves, interactions of 393—430
Gravitational waves, interactions of, with background curvature 427
Gravitational waves, interactions of, with coupled masses 436—441
Gravitational waves, interactions of, with electromagnetic waves 417—419
Gravitational waves, interactions of, with matter 419—427 441—442
Gravitational waves, metric for weak 396
Gravitational waves, phase velocity of 424 427 499
Gravitational waves, plane 435
Gravitational waves, power flux 438
Gravitational waves, tail of 429
gyromagnetic ratio 217 218
Gyroscope experiment 486—487
Half (conformally) flat space-times 234 235 310 311—320 see "Right
Hawking effect 144 169 348
Hawking effect and the second law of thermodynamics 147
Hawking effect and weak cosmic censorship 176
Heat, flux, conditions for absence of 500 501
Heat, inertia of 500
Heat, speed of 493 522—523
Heavenly angular momentum 83
Heavenly energy-momentum 84
Heavenly equation, first 251
Heavenly equation, second 252
Heavenly equation, second, and Yang-Mills field 279
Hermitian form of Riemannian metric 224
Hermitian inner product 225
Hermitian manifold 225 235
Hermitian manifold, Ricci tensor for 227
Hermitian pseudospace 242
Hermitian spinor 285
Higgs field and the energy condition 149
Higgs field at  68
Holomorphic coordinate transformation 221 222
Holomorphic deformation of twistor space 234
Holomorphic functions 221
Holomorphic functions and  spaces 227—237
Holomorphic Riemannian metric 225 231
Holonomy group 257 266 267
Holonomy group, reduced 274
Homothetic Killing vector 258
Horizon, apparent 146
| Horizon, Cauchy 122 135 138 151 162
Horizon, Cauchy, stability of 167—176
Horizon, causality 123
Horizon, event 110 122 143 146 376 378
Horizon, event, and asymptotically flat stationary space-times 143
Horizon, event, and trapped surface 132 145
Horizon, event, destruction of, in Kerr — Newman metric 188
Horizon, event, generators of 145
Horizon, Killing 143
Horizon, Killing, bifurcation of 144
Horizon, particle 110 122
Horizon, particle, and background microwave radiation 142
Horizon, particle, and Bianchi cosmologies 142
Horizon, Schwarzschild 132 364 369
Hubble constant 331 324 336
Hubble relation 103 330
Hubble shift 104
Hubble sphere 340 350
Hubble time 429
Hydrogen, intergalactic 347—348
Hyperheavenly equation, expanding 271
Hyperheavenly equation, nonexpanding 268
Hyperheavenly spaces 263—279
Hyperheavenly spaces with two sets of null strings 274
Hyperheavenly spaces, electrovac 278
Hyperheavenly spaces, explicit solutions for 275—279
Hyperheavenly spaces, symmetries in 277
i 286 287
IF (irreducible future set) 155
Impulsive gravitational waves 310
Inertial material density 503
Initial data set, boosting of 38
Initial singularity 103 109 163
Instability of Cauchy horizon in anti-de Sitter space 152 171—172
Instability of Cauchy horizon in Taub — NUT space 152
IP (irreducible past set) 154
Isentropic changes of energy 504
Isentropic expansion, work done in 503
Isentropic flows 501 502
Israel — Carter — Robinson theorem 144 179 378
Kaehlerian form 226
Kaehlerian geometry and Maxwell field 236
Kaehlerian manifold 226 231 235
Kaehlerian metric 325
Kaehlerian scalar 226 325
Kaehlerian scalar, complex 235
Kaluza — Klein theory 108
Kerr congruence 230 231
Kerr factor 384
Kerr metric 21 66 80 128 214 218 220 359 378
Kerr metric and asymptotic predictability 145
Kerr metric and Cauchy surface 120
Kerr metric and causality violation 123
Kerr metric and domain of dependence 120
Kerr metric and fluid interior 89
Kerr metric and stability 179
Kerr metric, angular momentum of 74
Kerr metric, black hole 146 379—380
Kerr metric, energy of 74
Kerr metric, ergo region of 91 143 380
Kerr metric, matching of internal solution to external 88
Kerr theorem 218 229 230 305 310
Kerr theorem, hypersurface version 321
Kerr — Newman metric 151 152 359 378
Kerr — Newman metric and destruction of event horizon 188
Kerr — Newman metric and stability of Cauchy horizon 188
Kerr — Newman metric in tetrad form 215
Killing equation in spinorial form 258
Killing equation, conformal 258
Killing equation, conformal, on  17 18
Killing equation, master 262
Killing field, asymptotic 52
Killing field, timelike, and dipole angular momentum 61
Killing horizon see "Horizon"
Killing scalars 86 89 90
Killing spinor 259 261
Killing vector and axisymmetry 85
Killing vector and stationarity 85
Killing vector, commutation of 85
Killing vector, homothetic 258
Kinetic theory and derivation of transport equation 519—522
Kinetic theory, covariant 511—523
Kinnersley group 259
Klein representation of lines in 287
Kodaira theorem 313
Komar conservation laws 73
Komar integral 59 61 66 73 74 80
Komar integral in axisymmetric space-times 86
Komar integral, modified for 75—77
Lagrange's identity 309
Landau damping of electromagnetic waves in a plasma 424 429
Laser interferometer as gravitational wave antenna 443
Left (conformally) flat space 23 312 314
Lens-Thirring effect see "Dragging of inertial frames"
Lie group as symmetry group of space-time 125
Lie system of partial differential equations 262
Lienard-Wichart solutions, generalized 220
Light deflection by gravitational field 474—477
Limit of stress-energy tensor 54
Limit of tensor field 44
Limit, directional dependent 43
Limit, regular 44
Lindblom theorem 80
Liouville equation, relativistic and linearized 422
Liouville theorem 514 517
Liouville theorem for paraelectromagnetic dipole gas 518
Lorentz group 19 62
Lorentz group on Spi 53 59
Lorentz slice of a complex space-time 312
Ludvigsen's heavenly energy conservation 84
Mach's principle 71
Magnetic dipole in space 234
Magnetic-type gravitational force 92 93
Mass see also "Stress-energy tensor"
Mass in axisymmetric stationary space-times 86
Mass quadrupole gravitational antenna 437—441
Mass, aspect at 59
Mass, Bondi 15 76
Mass, quadrupole as gravitational antenna 437—441
Mass, radiated away 15
Mass, ratio of inertial to gravitational 470
Massless free field and twistors 296—297
Massless free-field equation 298
Massless free-field equation on half flat background 318
Massless free-field equation, generation of solutions 301
Massless free-field equation, left-handed potential for 320
Massless free-field equation, related to twistor equation 299—300
Massless particle and twistors 296—297
Matching of stationary interior solutions to stationary exterior 88
Maxwell field as example at 42
Maxwell field, polarization of 396
Maxwell field, stress-energy tensor in spin coefficient formalism 27
Maxwell — Lorentz equations 496
Maxwell's equations and Kaehlerian geometry 236
Maxwell's equations in spin coefficient formalism 320
Maxwell's equations, algebraically null solutions 227
Maxwell's equations, generation of solutions 320
Mechanical oscillator as gravitational wave detector 403—406
Mechanical oscillator, quantum theory of 406—409
Medium, deformation and torsion of 497
Medium, entropy flux in 497
Medium, equilibrium of 497—501
Medium, lattice points of 497
Medium, thermodynamics of a polarized 495—508
Metric equations of the spin coefficient formalism 24—25
Metrics, space-times, and cosmologies see also "Algebraically special space-times" "Cosmologies" "Kerr" "Reissner "Schwarzschild" "Taub
Metrics, space-times, and cosmologies, B1 209
Metrics, space-times, and cosmologies, Brill — Cohen 90
Metrics, space-times, and cosmologies, charged C 128
Metrics, space-times, and cosmologies, Goedel 89 111 112
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