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Paper   IPM / Physic / 6950
School of Physics
  Title:   Casimir Densities for A Spherical Shell in the Global Monopole Background
1.  A.A. Saharian
2.  M.R. Setare
  Status:   Published
  Journal: Classical Quant. Grav.
  No.:  10
  Vol.:  20
  Year:  2003
  Pages:   3765-3782
  Supported by:  IPM
We investigate the vacuum expectation values for the energymomentum tensor of a massive scalar field with general curvature coupling and obeying the Robin boundary condition on a spherical shell in the (D +1 -dimensional globalmonopole background. The expressions are derived for the Wightman function, the vacuum expectation values of the field square, the vacuum energy density, radial and azimuthal stress components in both regions inside and outside the shell. Aregularization procedure is carried out by making use of the generalized AbelPlana formula for the series over zeros of cylinder functions. This formula allows us to extract from the vacuum expectation values the parts due to the global monopole gravitational field in the situation without a boundary, and to present the boundary-induced parts in terms of exponentially convergent integrals, useful, in particular, for numerical calculations. The asymptotic behaviour of the vacuum densities is investigated near the sphere surface and at large distances. We show that for small values of the parameter describing the solid angle deficit in global monopole geometry the boundary-induced vacuum stresses are strongly anisotropic.

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