  We consider a solution of the effective four-dimensional Einstein equations,
obtained from the general relativistic Schwarzschild metric through the
principle of Minimal Geometric Deformation (MGD). Since the brane tension can,
in general, introduce new singularities on a relativistic E\"otv\"os brane
model in the MGD framework, we require the absence of observed singularities,
in order to constrain the brane tension. We then study the corresponding
Bose-Einstein condensate (BEC) gravitational system and determine the critical
stability region of BEC MGD stellar configurations. Finally, the critical
stellar densities are shown to be related with critical points of the
information entropy.
