Geodesic
Axisymmetric pure radiation space--time with causality-violating geodesics
Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 3, pp. 483-490

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We present a stationary axisymmetric space–time admitting circular closed timelike geodesics everywhere within a finite region of space. The space–time is free from curvature divergence and is locally isometric to a nonvacuum pp-wave space–time. The matter–energy content is a pure radiation field and satisfies the null energy condition (NEC), and the metric is of type N in the Petrov classification scheme. Finally, we demonstrate the existence of timelike and null circular geodesic paths for this metric.
Keywords: nonvacuum solution, causality violation, radiation field, pp-wave. 
@article{TMF_2018_195_3_a7,
     author = {F. Ahmed},
     title = {Axisymmetric pure radiation space--time with causality-violating geodesics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {483--490},
     publisher = {mathdoc},
     volume = {195},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a7/}
}
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F. Ahmed. Axisymmetric pure radiation space--time with causality-violating geodesics. Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 3, pp. 483-490. http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a7/