Summary
A complete classification of spherically symmetric space-times according to their isometries and metrics (or classes of metrics) is obtained by solving the Killing equations. It is demonstrated that a symmetry given by Turkowski does not correspond to any metric.
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Qadir, A., Ziad, M. The classification of spherically symmetric space-times. Nuov Cim B 110, 317–334 (1995). https://doi.org/10.1007/BF02741372
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DOI: https://doi.org/10.1007/BF02741372