Summary
A complete classification of static, cylindrically symmetric space-times according to their isometries and metrics (or classes of metrics) is obtained. Metrics with their Killing vectors and their Lie algebras are given explicitly.
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Qadir, A., Ziad, M. Classification of static cylindrically symmetric space-times. Nuov Cim B 110, 277–290 (1995). https://doi.org/10.1007/BF02741369
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DOI: https://doi.org/10.1007/BF02741369