The Zipoy-Voorhees q-metric has non-vanishing NP constants and serves as a counterexample showing that algebraic speciality is needed for vanishing NP constants in asymptotically flat stationary vacuum spacetimes.
Chowdhury, Mandar Patil, Daniele Malafarina, and Pankaj S
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Asymptotic charges of a quadrupolar naked singularity
The Zipoy-Voorhees q-metric has non-vanishing NP constants and serves as a counterexample showing that algebraic speciality is needed for vanishing NP constants in asymptotically flat stationary vacuum spacetimes.