  We show through Schwinger's approach that in a static weak gravitational
background, the Casimir Energy for a real massless scalar field obeying
Dirichlet boundary conditions on rectangular plates is unaltered from it's flat
space-time value. The result is obtained considering an rather general class of
backgrounds, adding further generality and consistency test for the previous
work. The proposed result has direct consequences on earlier works in the
literature that found gravity related corrections for similar setups.
