  We provide a $5D$ generalization of the Hawking {\it et al.} black string in
a Randall Sundrum setup. The embedded $4D$ geometry corresponds to the
Simpson-Visser (SV) spacetime, which can represent a traversable wormhole, a
one-way wormhole, or a regular black hole. To achieve this, we linearly deform
both the bulk geometry and the bulk matter distribution with respect to a
coupling constant. These deformations induce a transition from a $5D$ vacuum
AdS distribution to an anisotropic distribution. The latter results in the
induced geometry on the brane transitioning from a singular Schwarzschild
spacetime to a regularized SV spacetime. Since there are no sources or matter
fields on the brane, we can assert that the induced SV geometry on the brane
arises from the influence of geometrical and matter deformations in the bulk.
Thus, the central singularity is suppressed. We determine the cases where the
energy conditions are either satisfied or violated. Our spacetime is
asymptotically radial AdS, which is intriguing given the absence of a global
AdS box that would prevent instability under larger wavelength perturbations.
Therefore, it is no longer appropriate to claim that instability exists for
very small perturbations near the AdS horizon.
