Geodesic
Congruence convergence in pp-wave space--time
Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 2, pp. 269-287

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We argue that the well-known geodesic completeness property of pp-waves can be disregarded once the geodesics are extracted as being extended along sets of Brinkmann coordinates. We investigate this issue in the more general context of congruence convergence and show that the problem leads to various issues for nongeodesic congruences. Our consideration is mostly based on the null congruence expansion, and we also provide a generalized Raychaudhuri equation.
Keywords: gravitational wave, pp-wave, congruence expansion, generalized Raychaudhuri equation
Mots-clés : convergence. 
@article{TMF_2018_195_2_a7,
     author = {M. Fathi and M. Mohseni},
     title = {Congruence convergence in pp-wave space--time},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {269--287},
     publisher = {mathdoc},
     volume = {195},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_195_2_a7/}
}
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M. Fathi; M. Mohseni. Congruence convergence in pp-wave space--time. Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 2, pp. 269-287. http://geodesic.mathdoc.fr/item/TMF_2018_195_2_a7/