Contents

700 Indextype D solutions (contd)Robinson–Trautman pureradiation, 435twisting diverging Einstein–Maxwell, 461twisting pure radiation, 464twisting vacuum, 452vacuum Kundt’s class, 478vacuum of embedding class two,599vacuum Robinson–Trautman,425type N solutionsdiverging Einstein–Maxwell, 462Kerr–Schild, 496Kerr–Schild pure radiation, 499Kundt’s class Einstein–Maxwell,481Kundt’s class vacuum, 476perfect fluids, 515recurrent, 557Robinson–Trautman Einstein–Maxwell, 429Robinson–Trautman pure radiation,435Robinson–Trautman vacuum,424shearing pure radiation, 410twisting vacuum, 451vacuum Kerr–Schild, 492vacuum of embedding class two,599with a G 4 on T 3 , 186vacuum solutionsalgebraically special, 88colliding waves, 392, 394conformastationary, 287cylindrically-symmetric, 350homogeneous, 174, 175, 181Lewis’s class, 311of embedding class two, 598of Kerr–Schild type, 450of Kundt’s class, 475, 476of Robinson–Trautman type, 423Papapetrou’s class, 309plane-symmetric, 234static, 284static axisymmetric, 304stationary axisymmetric, 304,526stationary cylindricallysymmetric,343stationary with geodesiceigenrays, 282twisting, 437, 442type D, 412, 452, 478type N, 424, 451, 476Weyl’s class, 304with a G 3 on V 2 , 230with a G 3 on V 3 , 196with a G 4 on V 3 , 195with a null Killing vector, 136,380with a spacelike Killing vectorand geodesic eigenrays, 283with flat slices, 573with shearing null vector,414Vaidya solution, 231, 436, 489vector bundle, 27vector fieldsand Riemann tensor, 72conformal Killing, 565constant, 553geodesic, 68homothetic, 69, 564hypersurface-orthogonal, 68Killing, 69non-rotating, 68normal, 68null, 74, 75, 86recurrent, 69similarity, 564surface-forming, 69time-like unit, 70vectors, 12covariant, 14orthogonal, 31spacelike, timelike, null, 31