Casimir densities for a spherical shell in the global monopole background

Abstract

We investigate the vacuum expectation values for the energy-momentum 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 global monopole 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. A regularization procedure is carried out by making use of the generalized Abel-Plana 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 behavior 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.

19 pages, 4 figures, discussion of zeros is added, accepted for publication in Classical and Quantum Gravity

References in corpus (3)

• Zeta Functions and the Casimir Energy
• Casimir effect in de Sitter and Anti-de Sitter braneworlds
• The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect

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