The global existence, uniqueness and C^1-regularity of geodesics in nonexpanding impulsive gravitational waves

Article

The global existence, uniqueness and C^1-regularity of geodesics in nonexpanding impulsive gravitational waves

Podolský, J.; Sämann, C.; Steinbauer R.; Švarc, R.

Class. Quantum Grav. 32(2), 025003 (2015)

Abstract

We study geodesics in the complete family of nonexpanding 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 prove the existence and uniqueness of continuously differentiable geodesics (in the sense of Filippov) and use a C^1-matching procedure to explicitly derive their form.

Institute authors

Supported by

GACR 14-37086G — Albert Einstein Center for Gravitation and Astrophysics
UNCE 204020/2012 — Výzkum Země a vesmíru metodami teoretické, počítačové a experimentální fyziky

BibTeX

@article{UTF519,
  author        = {Podolský, J. and Sämann, C. and Steinbauer R. and Švarc, R.},
  title         = {{The global existence, uniqueness and C\textasciicircum{}1-regularity of geodesics in nonexpanding impulsive gravitational waves}},
  journal       = {Class. Quantum Grav.},
  volume        = {32},
  number        = {2},
  pages         = {025003},
  year          = {2015},
  month         = {1},
  doi           = {http://dx.doi.org/10.1088/0264-9381/32/2/025003},
  eprint        = {1409.1782},
  archivePrefix = {arXiv},
}