Gravity and Strings

674 Index
Einstein (cont.)
equations, 45, 46, 101, 114, 118, 120, 121, 123, 174, 176, 180,
182, 190, 197, 200, 202, 209–211, 213, 238, 541
cosmological, 102, 104, 106, 109, 112
from string theory, 434
in CSK theory, 133, 134, 138, 140
in dilaton a-model, 350, 351
in Einstein–Maxwell theory, 227
in Einstein–Maxwell theory (duality-invariant form), 246
in Kaluza–Klein (KK) theories, 302
in purely affine theory of gravity, 126
in supergravity theories, 156, 159, 165, 168
in the Einstein-scalar theory, 214
interpretation of solutions, 187
not solved at singular points, 200
of NGT, 124
vacuum, 92, 93, 96, 126, 188
with a Dirac spinor, 131
frame, 302, 304, 305, 313, 319, 342, 346, 357, 434, 447, 464,
471, 478, 482, 514, 540, 555
manifest duality-invariance of the action, 303, 448, 466, 489,
490, 549
versus string frame, 530, 548
frame (modified), 304, 305, 319, 322, 328, 335, 487, 536, 537,
541, 576, 581, 585
and definition of mass, 305, 548, 583
versus string frame, 530, 548
gauge, 57
medium-strong form of the PEGI, 99
metric, 121, 490, 516, 549, 578
duality invariance, 586
metric (modified), 549
non-symmetric gravity theory, see non-symmetric gravity
theory)
scalar theories of gravity, 46
space, 547, 563, 637
teleparallelism theories of gravity, 145
tensor, 9, 12, 13, 40, 96, 101, 133, 138
cosmological, 104, 106, 177
for the Reissner–Nordström (RN) metric, 239
for the Schwarzschild metric, 202
transformation under Weyl rescalings, 639
Einstein–Fokker theory, 55–57
Einstein–Hilbert action, 46, 96, 102, 114, 115, 274
and Komar’s formula, 177
and Palatini’s identity, 638
in dimensional reduction, 301, 333, 334, 436, 454,
471
and the string effective action, 431
boundary terms, 118
coupling to matter, 120
coupling to the Maxwell field, 218
dimensional reduction on S 1 , 299, 314
string frame, 436
dimensional reduction on T n , 332
Einstein versus string frames, 433, 530
Euclideanized, 203
first-order form, 96, 123–126
from gauge formulation, 144
in N = 1, d = 4 supergravity, 154
in 2d and Euler characteristic, 411
in CSK theory, 132, 134
for a Dirac spinor, 139
symmetries and gauge identities, 134–139
in teleparallel theories, 146, 148
Noether current, 120
purely affine form, 126
symmetries and gauge identities, 119
weak-field expansion, 107–108
Einstein–Infeld–Hoffmann method, 402
Einstein–Maxwell theory, 213, 218–227, 279, 285, 286, 350
and N = 2, d = 4 supergravity, 373
and electric–magnetic duality, 245–258
group, 246
equations of motion, 219, 227
equations of motion with sources, 238
generalized to N vectors, 237
in 4d, 310
and N = 2, d = 4 supergravity, 316
oxidation of solutions, 320
in 5d
and N = 1, d = 5 supergravity, 313
in higher d, 263, 317
dimensional reduction, 291, 313–315
equations of motion, 263
oxidation of solutions, 320
reduction of solutions, 317
most general BH solutions, 262
with θ-term, 256–258
Einstein–Maxwell-dilaton theory, see dilaton a-model
Einstein-scalar theory
Einstein-Hilbert action, 20
and Komar’s formula, 180
Euclideanized, 208
Einstein–Infeld-Hoffmann method, 413
in 4d, 214–218
in higher d, 262
oxidation of solutions, 326
JNW solutions, see solution, Janis–Newman–Winicour
Einstein–Straus–Kaufman theory, 124
Einstein–Yang–Mills theories, 215
Elfbein, 449
energy–momentum tensor
Belinfante, see Belinfante
canonical, 26, 29, 31, 39, 47, 56, 68, 80, 133, 135
covariant, 129, 136, 140
for a scalar field, 33
of the FP theory, 79,81
relation to the Vielbein energy–momentum tensor, 134
symmetrization and Belinfante tensor, 34, 35–37
for a (p + 1)-form potential, 22, 23
for the gravitational field in teleparallelism theories, 145
improved, 37,38
Rosenfeld, see Rosenfeld
super-energy–momentum tensors, 171
Vielbein, see Vielbein, energy–momentum tensor
equivalence principle of gravitation and inertia, 99
ERN, see solution, extreme Reissner–Nordström (RN)
Euler characteristic
in 4d, 144
Euler angles, 392, 603, 604
Euler characteristic
in 2d, 412, 425
in 4d, 243, 274
with boundary terms, 243
Euler–Lagrange equations, 10, 27,33
event horizons
and Killing horizons, 197
exterior derivative, 6, 23
F1 solution, see solution, F1
Ferrara, 164
Feynman, 45, 46, 59, 95
diagrams in string theory, 409, 412
Fierz
identities, 158, 159, 167, 169, 182
genera, 620
in N = 2, d = 4 supergravity, 620
in 4d, 625
Fierz–Pauli Lagrangian, 44–46, 58, 59, 63, 63–96, 101, 114
and non-symmetric gravity theories (NGT), 124
and string theory, 405
coupling to matter, 67–76
consistency, 76