Abstract
We study conformal vector fields and their zeros on spacetimes which are non-conformally-flat. Depending on the Petrov type, we classify all conformal vector fields with zeros. The problems of reducing a conformal vector field to a homothetic vector field are considered. We show that a spacetime admitting a proper homothetic vector field is (locally) a plane wave. This precises a well-known theorem of {Alekseevski}, where all these spacetimes are determined in a more general form.
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Steller, M. Conformal vector fields on spacetimes. Ann Glob Anal Geom 29, 293–311 (2006). https://doi.org/10.1007/s10455-005-9001-9
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DOI: https://doi.org/10.1007/s10455-005-9001-9