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arXiv · 1602.05020

The global uniqueness and $C^1$-regularity of geodesics in expanding impulsive gravitational waves

Jiri Podolsky·Clemens Sämann·Roland Steinbauer·Robert Svarc
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Abstract

We study geodesics in the complete family of expanding impulsive gravitational waves propagating in spaces of constant curvature, that is Minkowski, de Sitter and anti-de Sitter universes. Employing the continuous form of the metric we rigorously prove existence and global uniqueness of continuously differentiable geodesics (in the sense of Filippov) and study their interaction with the impulsive wave. Thereby we justify the "$C^1$-matching procedure" used in the literature to derive their explicit form.

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Jiri Podolsky, Clemens Sämann, Roland Steinbauer, Robert Svarc. 2016-02-16. The global uniqueness and $C^1$-regularity of geodesics in expanding impulsive gravitational waves. https://doi.org/10.1088/0264-9381/33/19/195010

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