  This work is devoted to provide a way of representing $4D$ spherically
symmetric and static compact stellar configurations into a $5D$ space time,
using the black string framework.
  We write the four and five dimensional line elements and the four and five
dimensional energy momentum tensor such that the four and five dimensional
quantities are related by a function $A(z)$, where $z$ represents to the extra
dimension. Remarkably, one consequence of our chosen form for the line element,
for the energy momentum tensor and for $A(z)$, is the fact that the $5D$
equations are reduced to the usual form of the four dimensional equations of
motion. Also, the five dimensional conservation equation adopts the form of the
four dimensional conservation equation. It is worth mentioning that, although
our methodology is simple, this form of reduction could serve to represent
other types of four dimensional objects into an extra dimension in future
works. Furthermore, under our assumptions the sign of the pressure along the
extra dimension is given by the trace of the four dimensional energy momentum
tensor.
  Furthermore, our simple election for the function $A(z)$ modifies some
features of the induced 4--dimensional compact stellar configuration, such as
the mass--radius relation, the momentum of inertia, the central values of the
thermodynamic variables, to name a few. Besides, the topology of this model is
${S}^{2}\times {S}^{1}$ and not the ${S}^{3}$ topology of the 5--dimensional
structures.
