Localized Five‐Dimensional Rotating Brane‐World Black Hole Analytically Connected to an to an AdS ₅ Boundary

ABSTRACT We provide a method to describe the geometry of an analytic, exponentially localized rotating braneworld black hole using the Janis–Newman algorithm in Hopf coordinates. The induced metric on the brane matches the standard Kerr spacetime. Two curvature singularities arise: one confined to the 3‐brane at , and another that, on the brane, reproduces the Kerr singularity at , . The inner and event horizons, together with the stationary limit hypersurfaces, extend into the extra dimension in a pancake‐like shape. We describe their behavior in the bulk. The energy–momentum tensor represents a source transitioning from an anisotropic, nondiagonal structure to a vacuum with a negative cosmological constant. Thus, the localized black hole connects to an AdS 5 boundary. The geometry is supported by a nondiagonal anisotropic fluid in the bulk, requiring no matter on the brane. To evaluate the energy conditions, we use a one‐form from the dual basis that yields a diagonal energy–momentum tensor. The energy conditions are satisfied close to the brane, while they are violated at a location outside the brane but within the extension of the event horizon. The latter is required to support the rotating geometry.