Gravity and Strings

682 Index
solution (cont.)
Robinson–Bertotti (RB), 235, 286, 382, 399, 519
Reissner–Nordström (RN), 196, 203
as a vacuum of N = 2, d = 4 SUEGRA, 386
dyonic in 4d, 394
electric, in 4d, 235
electric, in higher d, 266
in 4d Euclidean, 242
symmetry superalgebra, 386–388, 608
Sp (black), 531
S5, 537
S5 (black), 537
Schwarzschild, 187–212, 215, 216, 225, 228, 230, 234, 236, 238,
240, 242, 578
4d entropy, 204
4d temperature, 204
ADM mass, 189
and supersymmetry, 398
as an eternal BH, 194
as Weyl’s axisymmetric vacuum solution, 324
boosting, 286
derived, 188
dimensional oxidation of, 326
dimensional reduction of, 323–326
entropy in higher d, 212
horizon area, 197
horizon area in higher d, 212
in 4d Eddington–Finkelstein coordinates, 191
in 4d Euclidean, 209–210, 242, 273
in 4d Euclidean action, 211
in 4d harmonic coordinates, 200
in 4d isotropic coordinates, 198
in 4d Kruskal–Szekeres coordinates, 193, 194
in 4d Schwarzschild coordinates, 176, 179, 188, 268, 269
in higher d, 211, 263, 264, 352, 512, 578
in string theory, 405
interior, 190
Penrose diagram, 193
periodic arrays of, 325
perturbations of, 195
perturbative expansion, 88
singularities, 190–192, 230, 238
sources, 200–202
specific heat, 205
stability, 189
surface gravity, 198
temperature in higher d, 212
thermodynamics, 202–211, 241, 356
with negative mass, 195
Schwarzschild p-branes, 326, 331, 512–514, 515
instability of, 513–514
tension, 513
SWIP, 363–368, 544, 588
as N = 2, d = 4 supergravity solutions, 367–368
as solutions of N = 4, d = 4 supergravity, 400
duality properties, 366
entropy and N = 4, d = 4 central charges, 401
general, 363–365
horizon area, 365
supersymmetric, 365–366
Taub-bolt, 273
as a Bianchi IX gravitational instanton, 278
Taub–NUT, 267–271
charged, 268
electrically charged, 280
extreme electrically charged, 280
in Schwarzschild coordinates, 269
interior solutions, 271
Weyl’s axisymmetric vacuum, 323
boosting, 286
higher-d generalizations, 326
Schwarzschild solution, 324
Weyl’s static axisymmetric electrovacuum, 228
solvable, see Lie, algebra, solvable
Sommerfield, see Bogomol’nyi–Prasad–Sommerfield (BPS)
Sorkin, 272, 291, 329
space
affinely connected, 6
cotangent, see cotangent space
maximally symmetric, 605
Riemann, see Riemann, space
Riemann–Cartan, see Riemann–Cartan spacetime
tangent, see tangent space
Weitzenböck, see Weitzenböck, spacetime
special geometry, 367–368
special-relativistic field theory (SRFT), 26, 32, 33, 45–47, 49, 51,
53, 55, 57–61, 63, 65, 67–73, 75, 77–79, 81, 83, 85, 87, 89,
91, 93, 95, 96, 100, 112, 171, 173, 200
special-relativistic quantum-field theory (SRQFT), 95, 112
specific heat
dilaton a-model BH, 356
Reissner–Nordström (RN) BH, 213, 241
Schwarzschild BH, 205
spin–energy potential, 34, 36, 41, 131, 135, 136
spin–energy potnetial, 133
spinning particle, 413
spinor, 601
Dirac, see Dirac, spinor
Majorana, see Majorana, spinor
Majorana–Weyl, see Majorana–Weyl, spinor
symplectic-Majorana, 618, 629
Weyl, see Weyl, spinor
squashed
S 3 and S 7 , 637
spheres, 609
Stückelberg
field, 226, 227, 258, 259, 296, 314, 341, 342, 345, 465
Stokes’ theorem, 24, 29, 31, 32, 175, 178, 181, 222, 223, 250, 255,
257, 276, 306, 507, 508
and the Gauss–Ostrogradski theorem, 24
Straus, see Einstein–Straus–Kaufman
string
USp(32) theory, 498
coupling constant, 116, 412, 420, 425, 431, 456, 487
heterotic theories, 423
length, 116, 292, 409, 430, 431, 520, 527, 547, 577, 582
versus 11d Planck length, 524
versus Planck length, 405
mass, 409
metric, 121
oriented, 411
singularity, see Dirac, string singularity
type-I theories, 423
type-I ′ theory, 499
type-IIA theories, 422
type-IIB theories, 422
unoriented, 411
Strominger, 515
Strominger–Vafa paper, 579
SUEGRA, see supergravity theories, extended
SUGRA, see supergravity theories
Sundrum, see Randall–Sundrum scenarios
mechanism, 346, 465
supergravity theories, 113, 126, 132, 313, 349, 354, 358, 359,
369–371, 373, 375, 380, 405, 413, 417, 424
N = 2, d = 4 supergravity and special geometry, 367
and the WNI technique, 181, 395
as effective string theories, 290, 406–408, 432, 435
as supergroup gauge theories, 140, 142, 151–155
and supersymmetric solutions, 557–559
Bogomol’nyi (or BPS) bounds, see Bogomol’nyi (or BPS)
bounds
bosonic truncation, 373
de Sitter (anti-), 143, see de Sitter (anti-)defined, 150