Geodesic motion in the Kundt spacetimes and the character of envelope singularity

Details Geodesic motion in the Kundt spacetimes and the character of envelope singularity Geodesic motion in the Kundt spacetimes and the character of envelope singularity

2004-04-15

arxiv.org/abs/gr-qc/0404068v1

Class.Quant.Grav. 21 (2004) 2811-2830

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages, 3 figures. To appear in Class. Quantum Grav

Scientific paper

10.1088/0264-9381/21/12/003

We investigate geodesics in specific Kundt type N (or conformally flat) solutions to Einstein's equations. Components of the curvature tensor in parallelly transported tetrads are then explicitly evaluated and analyzed. This elucidates some interesting global properties of the spacetimes, such as an inherent rotation of the wave-propagation direction, or the character of singularities. In particular, we demonstrate that the characteristic envelope singularity of the rotated wave-fronts is a (non-scalar) curvature singularity, although all scalar invariants of the Riemann tensor vanish there.

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