  Wightman function, the vacuum expectation values (VEVs) of the field squared
and the energy-momentum tensor are investigated for a massive scalar field with
general curvature coupling in a spherically symmetric static background
geometry described by two distinct metric tensors inside and outside a
spherical boundary. The exterior and interior geometries can correspond to
different vacuum states of the same theory. In the region outside the sphere,
the contributions in the VEVs, induced by the interior geometry, are explicitly
separated. For the special case of the Minkowskian exterior geometry, the
asymptotics of the VEVs near the boundary and at large distances are discussed
in detail. In particular, it has been shown that the divergences on the
boundary are weaker than in the problem of a spherical boundary in Minkowski
spacetime with Dirichlet or Neumann boundary conditions. As an application of
general results, dS and AdS spaces are considered as examples of the interior
geometry. For AdS interior there are no bound states. In the case of dS
geometry and for nonminimally coupled fields, bound states appear for a radius
of the separating boundary sufficiently close to the dS horizon. Starting from
a critical value of the radius the Minkowskian vacuum in the exterior region
becomes unstable. For small values of the AdS curvature radius, to the leading
order, the VEVs in the exterior region coincide with those for a spherical
boundary in Minkowski spacetime with Dirichlet boundary condition. The
exceptions are the cases of minimal and conformal couplings: for a minimal
coupling the VEVs are reduced to the case with Neumann boundary condition,
whereas for a conformally coupled field there is no reduction to Dirichlet or
Neumann results.
