Abstract
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.
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Most textbooks on general relativity provide extensive information on linearized gravity and the TT gauge (see, e.g., the relevant chapters in [2], [4], [5]).
Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 195, No. 2, pp. 269–287, May, 2018.
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Fathi, M., Mohseni, M. Congruence Convergence in Pp-Wave Space–Time. Theor Math Phys 195, 729–744 (2018). https://doi.org/10.1134/S0040577918050082
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DOI: https://doi.org/10.1134/S0040577918050082