Symmetries and geodesics in (anti-)de Sitter spacetimes with nonexpanding impulsive waves

Abstract

We consider a class of exact solutions which represent nonexpanding impulsive waves in backgrounds with nonzero cosmological constant. Using a convenient 5-dimensional formalism it is shown that these spacetimes admit at least three global Killing vector fields. The same geometrical approach enables us to find all geodesics in a simple explicit form and describe the effect of impulsive waves on test particles. Timelike geodesics in the axially-symmetric Hotta-Tanaka spacetime are studied in detail. It is also demonstrated that for vanishing cosmological constant, the symmetries and geodesics reduce to those for well-known impulsive pp-waves.

arXiv comment16 pages, 3 figures, LaTeX 2e. To appear in Class. Quantum Grav

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Cited by in corpus (24)

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• Memory Effect for Impulsive Gravitational Waves
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• Exact impulsive gravitational waves in spacetimes of constant curvature
• Ultrarelativistic black hole in an external electromagnetic field and gravitational waves in the Melvin universe
• Memory Effect and BMS-like Symmetries for Impulsive Gravitational Waves
• Refraction of geodesics by impulsive spherical gravitational waves in constant-curvature spacetimes with a cosmological constant
• Kundt geometries and memory effects in the Brans-Dicke theory of gravity
• Memory effects in Kundt wave spacetimes
• The global existence, uniqueness and C^1-regularity of geodesics in nonexpanding impulsive gravitational waves
• Memory effect and BMS symmetries for extreme black holes
• Ultrarelativistic boost of the black ring
• Memory Effect in Anti-de Sitter Spacetime
• Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, Part I
• The regularity of geodesics in impulsive pp-waves
• Soldering freedom and BMS-like transformations
• Catalysis of Black Holes/Wormholes Formation in High Energy Collisions
• Cut-and-paste for impulsive gravitational waves with $\Lambda$: The geometric picture
• Penrose junction conditions extended: impulsive waves with gyratons
• Penrose junction conditions with $\Lambda$: Geometric insights into low-regularity metrics for impulsive gravitational waves
• Kundt wave geometries in Eddington-inspired Born-Infeld gravity: New solutions and memory effects
• Riemann curvature of a boosted spacetime geometry
• Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, II
• Cut-and-paste for impulsive gravitational waves with $\Lambda$: The mathematical analysis