Multiple independent swirling parameters in higher dimensions

Construct a \(D\)-dimensional swirling spacetime with \(\lfloor(D-1)/2\rfloor\) independent swirling parameters \(j_i\).

Background

The paper gives a straightforward higher-dimensional extension of the five-dimensional swirling background in which the additional dimensions are inert and only one swirling parameter appears. A more substantial generalization would associate independent swirling parameters with the available rotational planes.

The authors suggest that a matrix Ernst equation could provide the necessary solution-generating framework by extending the Ehlers transformation to multiple independent parameters, but whether such a generalized Ernst symmetry exists and produces the desired solutions is unresolved.