Abstract
Empty space algebraically special metrics possessing an expanding degenerate principal null vector and a Killing vector are investigated. It is shown that the Killing vector falls into one of two classes. The class containing all asymptotically timelike Killing vectors is investigated in detail and the associated metrics are identified. Several theorems concerning these metrics are given, among which is a proof that if the metric is regular and possesses an asymptotically timelike Killing vector, then it must be typeD. In addition some relations between Killing vectors in general spaces are developed along with a set of tetrad symmetry equations stronger than those of Killing.
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Held, A. Killing vectors in empty space algebraically special metrics. I. Gen Relat Gravit 7, 177–198 (1976). https://doi.org/10.1007/BF00763434
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DOI: https://doi.org/10.1007/BF00763434