Contents

694 IndexHarrison solutions, 272Harrison transformation, 521for colliding waves, 402Hauser solution, 451radiating, 466, 469Herlt’s class, 320Hirota’s direct method, 152HKX transformations, 535applications of, 537holonomic frame, 12, 33holonomy, 26homogeneous space, 99homogeneous space-time, 157, 171with boost symmetry, 172with null rotation symmetry,171with rotation symmetry, 172homothetic vector, 110and similarity reduction, 132homothety, 98homothety groups, 110horizontal, 28hypersurface, 11hypersurface-homogeneous spacetimes,157, 183hypersurface-orthogonal vector field,68ideal, 94impulsive waves, 388incoherent radiation, 66initial value problemfor colliding waves, 387, 389integral manifold, 137invariant subgroup, 94invariants, 112, 113algebraically independent, 113Cartan, 116of the Ricci tensor, 114of the Riemann tensor, 114of the Weyl tensor, 114scalar, 113scalar polynomial, 114isogroup, 140isometry, 98isometry groups, 91determination of theirdimensions, 120isotropic coordinates, 227, 233, 249,296isotropy group, 99, 228isotropy of pressure, condition of, 248isovector, 140Israel–coordinates, 234Jacobi identity, 13jet bundle, 29, 137junction conditions, 45Kantowski–Sachs solutions, 185, 215,243Kasner metric, 197, 426Kerr solution, 311, 449, 453, 493radiating, 465, 498Kerr–Newman solutions, 325superposition of, 327Kerr–Schild metrics, 485Einstein–Maxwell, 493, 495energy-momentum tensor, 488generalized, 499geometrical interpretation, 487of Kundt’s class, 481pure radiation, 497special, 490twisting pure radiation, 465vacuum, 450, 492Khan–Penrose solution, 392Killing bivector, 99Killing equation, xxixKilling tensor, 559–561of perfect fluid solutions, 562of type D vacuum solutions,561Killing vectorand similarity reduction, 132cyclic, 293Killing–Yano tensor, 559, 560, 562of type D space-times, 563kinematic self-similarity, 564Kinnersley’s photon rocket, 435, 489Kinnersley–Chitre B-group, 535