Higher-dimensional Zipoy–Voorhees vacuum solution

Construct a higher-dimensional (dimension greater than four) Zipoy–Voorhees vacuum solution of Einstein’s equations to enable the formulation of general Zipoy–Voorhees–Fisher–Janis–Newman–Winicour (ZV–FJNW) spacetimes in arbitrary dimensions.

Background

In the five-dimensional static limit of the authors’ rotating Einstein–Scalar solutions, the geometry exhibits features akin to a Zipoy–Voorhees–FJNW configuration, with scalar-induced multipolar modifications. Extending this intuition more broadly would benefit from a genuine higher-dimensional Zipoy–Voorhees vacuum background.

The authors note that such higher-dimensional Zipoy–Voorhees vacuum solutions have not, to their knowledge, been constructed in the literature, which prevents formulating general ZV–FJNW spacetimes in arbitrary dimensions.