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Symmetries and the Karlhede classification of type N vacuum solutions

The influence of symmetries on the invariant classification of a general type N vacuum spacetime is studied. It is shown that the existence of two independent symmetries (Killing vector fields/homothetic vector fields) reduces the upper bound on the Karlhede algorithm for such solutions from five to three (derivatives), as long as the vector fields obey a geometrical condition obtained here. The only known twisting type N vacuum metric, the Hauser metric, is such an example.