  The one loop effective action in a Schwarzschild background is here used to
compute the Zero Point Energy (ZPE) which is compared to the same one generated
by a gravastar. We find that only when we set up a difference between ZPE in
these different background we can have an indication on which configuration is
favored. Such a ZPE difference represents the Casimir energy. It is shown that
the expression of the ZPE is equivalent to the one computed by means of a
variational approach. To handle with ZPE divergences, we use the zeta function
regularization. A renormalization procedure to remove the infinities together
with a renormalization group equation is introduced. We find that the final
configuration is dependent on the ratio between the radius of the wormhole
augmented by the "brick wall" and the radius of the gravastar.
