Geodesics for impulsive gravitational waves and the multiplication of distributions

Details Geodesics for impulsive gravitational waves and the multiplication of distributions Geodesics for impulsive gravitational waves and the multiplication of distributions

1996-07-30

arxiv.org/abs/gr-qc/9607076v1

Class.Quant.Grav. 14 (1997) 455-462

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, latex2e, amstex macros, no figures

Scientific paper

10.1088/0264-9381/14/2/018

We consider particle trajectories in the gravitational field of an impulsive
pp-wave. Due to the distributional character of the wave profile one inevitably
encounters an ambiguous point value $\theta(0)$. We show that this ambiguity
may be resolved by imposing covariant constancy of the square of the tangent.
Our result is consistent with Colombeau's multiplication of distributions.

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