Penrose junction conditions with $\Lambda$: Geometric insights into low-regularity metrics for impulsive gravitational waves

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 nonexpanding waves which later have been generalized to impulses traveling in all constant-curvature backgrounds, i.e., 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 recently a comparably powerful visualization and understanding has been missing in the case with a cosmological constant $\Lambda \ne 0$. Here we review the original Penrose construction and its generalization to non-vanishing $\Lambda$ in a pedagogical way, as well as the recently established visualization: A special family of global null geodesics defines an appropriate comoving coordinate system that allows to relate the distributional to the continuous form of the metric.

arXiv commentTo appear in the topical volume "Singularity theorems, causality, and all that (SCRI21)" https://link.springer.com/collections/hjjgajaagg honoring Roger Penrose's accomplishments in mathematical relativity; final corrected version, 27 pages, 7 figures

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