  We compute the Zero Point Energy (ZPE) induced by a naked singularity with
the help of a reformulation of the Wheeler-DeWitt equation. A variational
approach is used for the calculation with Gaussian Trial Wave Functionals. The
one loop contribution of the graviton to the ZPE is extracted keeping under
control the UltraViolet divergences by means of a distorted gravitational
field. Two examples of distortion are taken under consideration: Gravity's
Rainbow and Noncommutative Geometry. Surprisingly we find that the ZPE is no
more singular when we approach the singularity.
