Cut-and-paste for impulsive gravitational waves with $\Lambda$: The geometric picture

Abstract

Impulsive gravitational waves in Minkowski space were introduced by Roger Penrose at the end of the 1960s, and have been widely studied over the decades. Here we focus on non-expanding waves which later have been generalised to impulses travelling in all constant-curvature backgrounds, that is also the (anti-)de Sitter universe. While Penrose's original construction was based on his vivid geometric `scissors-and-paste' approach in a flat background, until now a comparably powerful visualisation and understanding have been missing in the $\Lambda \ne 0$ case. In this work we provide such a picture: The (anti-)de Sitter hyperboloid is cut along the null wave surface, and the `halves' are then re-attached with a suitable shift of their null generators across the wave surface. This special family of global null geodesics defines an appropriate comoving coordinate system, leading to the continuous form of the metric. Moreover, it provides a complete understanding of the nature of the Penrose junction conditions and their specific form. These findings shed light on recent discussions of the memory effect in impulsive waves.

arXiv commentfinal version, minor revision, 12 pages, 2 figures

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Cited by in corpus (8)

• Avoiding singularities in Lorentzian-Euclidean black holes: the role of atemporality
• Memory Effect and BMS-like Symmetries for Impulsive Gravitational Waves
• Null shells: general matching across null boundaries and connection with cut-and-paste formalism
• Penrose junction conditions with $\Lambda$: Geometric insights into low-regularity metrics for impulsive gravitational waves
• General matching across Killing horizons of zero order
• Gluing of Lorentzian length spaces and the causal ladder
• Cut-and-paste for impulsive gravitational waves with $\Lambda$: The mathematical analysis
• General Shells and Generalized Functions