  In this paper, we consider the Casimir energy of massless scalar field which
satisfy Dirichlet boundary condition on a spherical shell. Outside the shell,
the spacetime is assumed to be described by the Schwarzschild metric, while
inside the shell it is taken to be the flat Minkowski space. Using zeta
function regularization and heat kernel coefficients we isolate the divergent
contributions of the Casimir energy inside and outside the shell, then using
the renormalization procedure of the bag model the divergent parts are
cancelled, finally obtaining a renormalized expression for the total Casimir
energy.
