  We compute Zero Point Energy in a spherically symmetric background with the
help of the Wheeler-DeWitt equation. This last one is regarded as a
Sturm-Liouville problem with the cosmological constant considered as the
associated eigenvalue. The graviton contribution, at one loop is extracted wit
the help of a variational approach together with Gaussian trial functionals.
The divergences handled with a zeta function regularization are compared with
the results obtained using a Noncommutative Geometry (NCG) and Modified
Dispersion Relations (MDR). In both NCG and MDR no renormalization scheme is
necessary to remove infinities in contrast to what happens in conventional
approaches.
