Contents

Index 695Kinnersley–Chitre solution, 313, 316Kramer-Neugebauer transformation,528Kronecker delta, xxviiKruskal–Szekeres coordinates, 233Kundt’s class, 470Kundt–Thompson theorem, 89Kustaanheimo–Qvist solutions, 256Λ-term solutionshomogeneous, 180, 181of Kundt’s class, 483of Robinson–Trautman type, 436plane-symmetric, 235stationary cylindricallysymmetric,343with a G 3 on V 2 , 230with a G 3 on V 3 , 199Lanczos potential, 43left translation, 92Lemaitre–Novikov coordinates, 233Levi–Civita solution, 343Levi-Civita tensor, xxviii, 35Lewis’s class of vacuum solutions, 311Lie algebras, 91, 93ideal, 94Lie derivative, 21Lie groups, 91Lie point symmetry, 129, 131generator of, 130Lie transport, 22Lie’s theorems, 93, 98Lie–Bäcklund symmetry, 134, 140lifted curve, 28limiting proceduresfor type D Einstein–Maxwellfields, 323limits of families of space-times, 126line element, 31linear isotropy group, 99linear problem, 532Lorentz frame, 31Lorentz transformations, 32Lorentzian metric, 30LRS space-time, 160main equations, 437manifold, 10boundary of a, 21differentiable, 10orientable, 11mass function, 228Maxwell equationsin Newman–Penrose formalism,80Maxwell fieldenergy-momentum tensor, xxix,61null and non-null, 62null tetrad components, xxixRainich conditions, 64McVittie solution, 258Melvin solution, 345metric condition, 33metric tensor, 30Misner’s parametrization, 189Morgan–Morgan disk, 308motions, 98conformal, 564, 565, 567multipole moments for stationaryvacuum solutions, 289n-bein, 13Neugebauer–Meinel solution, 548Newman–Penrose equations, 75, 79integrability conditions, 82, 83Newman–Tamburino solutions, 414Noether’s theorem, 149normal vector field, 68normal-hyperbolic, 30null dust, 61null Killing vector, 379non-twisting, 380null rotation, 32, 160null rotation isotropy, 186null surface, 375null tetrad, xxviii, 31null vector fields, 70geodesic, 86geodesic and shearfree, 87,491