Casimir densities from coexisting vacua

Abstract

The 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, de Sitter (dS) and anti--de Sitter (AdS) spaces are considered as examples of the interior geometry. For AdS interiors 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 a 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 a Neumann boundary condition, whereas for a conformally coupled field there is no reduction to Dirichlet or Neumann results.