Contents

Index 693with a G 4 on S 3 or T 3 , 195with a magnetic dipole, 321with a null Killing vector, 380,382with diverging twisting rays, 455,458Einstein–Maxwell null fields, 88Einstein–Rosen waves, 352Einstein–Straus model, 47elementary flatness, 292Ellis classes, 162embedding, 580global isometric, 581local isometric, 580embedding class, 580, 583≥ 2, 603and groups of motion, 585, 586and special vector fields, 584energy conditions, 63energy-momentum tensor, xxix, 60and groups of motions, 611, 612equivalence method of Cartan, 116equivalence of space-times, 112, 116Ernst equation, 299for colliding waves, 390, 392, 400Ernst–Wild solution, 326expansionof a time-like unit vector field, 70exterior curvature, 572exterior derivative, 18exterior product, 17Farnsworth–Kerr classes, 178fibre bundles, 27forms1-forms, 132-forms, 20p-forms, 17rank of a 2-form, 20simple, 18frame bundle, 27Friedmann universe, 212Frobenius’s theorem, 19γ-law, 66Gauss equations, 572, 582Gaussian curvature, 101generalized orthogonal group, 99generation methodsfor Einstein–Maxwell fields, 550for electrovac with one Killingvector, 518for perfect fluids, 152for two spacelike Killing vectors,550generatorof a point transformation, 130geodesic, 33geodesic null vector fields, 70, 86rotation, shear and expansion of,71Geroch conjecture, 547Geroch group, 146GHP formalism, 84Gödel solution, 177, 178, 576Goldberg–Sachs theorem, 87Gowdy universes, 351group parameters, 91groupsAbelian, 94derived, 94G 2 , G 3 ,95G 4 ,96G 5 ,97semisimple, 94simple, 94solvable, 94transitive, 97groups of motions, 98and energy-momentum tensors,611, 612and Petrov types, 606, 609, 610maximal, 100multiply-transitive, 106on non-null orbits, 264on null orbits, 375orbits of, 104simply-transitive, 105half null tetrad, 32harmonic map, 148, 518