H. Balasin, GEODESICS FOR IMPULSIVE GRAVITATIONAL-WAVES AND THE MULTIPLICATION OFDISTRIBUTIONS, Classical and quantum gravity, 14(2), 1997, pp. 455-462
We consider particle trajectories in the gravitational field of an imp
ulsive pp-wave. Due to the distributional character of the wave profil
es, one inevitably encounters an ambiguous point value theta(0). We sh
ow 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.