Closed-form bulk completion of the rotating braneworld black hole

Construct a closed-form five-dimensional vacuum solution for a rotating black hole localized on the brane in the Randall–Sundrum II scenario, thereby providing the complete bulk geometry underlying the effective four-dimensional rotating braneworld geometry.

Background

The paper studies a rotating black-hole geometry induced on a brane in the Randall–Sundrum II model, where the influence of the five-dimensional bulk is represented in four dimensions by the projected Weyl tensor and a tidal charge. Although fully backreacted static and rotating braneworld solutions have been obtained numerically, the effective four-dimensional treatment used here avoids requiring an explicit bulk completion.

The unresolved issue is whether an analytic, closed-form five-dimensional vacuum geometry exists for a rotating black hole localized on the brane. Such a solution would clarify the bulk origin of the tidal charge and go beyond the induced Kerr–Schild geometry analyzed in the paper.