Geodesics and geodesic deviation for impulsive gravitational waves

Details Geodesics and geodesic deviation for impulsive gravitational waves Geodesics and geodesic deviation for impulsive gravitational waves

1997-10-28

arxiv.org/abs/gr-qc/9710119v2

J.Math.Phys. 39 (1998) 2201-2212

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

final version, minor grammatical changes

Scientific paper

The geometry of impulsive pp-waves is explored via the analysis of the geodesic and geodesic deviation equation using the distributional form of the metric. The geodesic equation involves formally ill-defined products of distributions due to the nonlinearity of the equations and the presence of the Dirac $\de$-distribution in the space time metric. Thus, strictly speaking, it cannot be treated within Schwartz's linear theory of distributions. To cope with this difficulty we proceed by first regularizing the $\de$-singularity,then solving the regularized equation within classical smooth functions and, finally, obtaining a distributional limit as solution to the original problem. Furthermore it is shown that this limit is independent of the regularization without requiring any additional condition, thereby confirming earlier results in a mathematical rigorous fashion. We also treat the Jacobi equation which, despite being linear in the deviation vector field, involves even more delicate singular expressions, like the ``square'' of the Dirac $\de$-distribution. Again the same regularization procedure provides us with a perfectly well behaved smooth regularization and a regularization-independent distributional limit. Hence it is concluded that the geometry of impulsive pp-waves can be described consistently using distributions as long as careful regularization procedures are used to handle the ill-defined products.

Affiliated with

Also associated with

No associations

Rating

Geodesics and geodesic deviation for impulsive gravitational waves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geodesics and geodesic deviation for impulsive gravitational waves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geodesics and geodesic deviation for impulsive gravitational waves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-481895