Quantum Vacuum Effects in the Gravitational Field of a Global Monopole

A study is made of the vacuum expectation values for the energy-momentum tensor of a massive scalar field that satisfy a Robin mixed boundary condition on a spherical surface with a background gravitational field from a D+1-dimensional global monopole. Expressions are derived for the Wightman function, vacuum expectation of the square of the field, vacuum energy density, and the radial and azimuthal pressures inside the spherical surface. The regularization procedure involves using the generalized Abel-Plana formula for series in terms of the zeroes of cylindrical functions. This formula makes it possible to separate the part owing to the gravitational field of a global monopole without boundaries from the vacuum expectation and to represent the parts induced by the boundary in the form of exponentially converging integrals which are especially convenient for numerical calculations. The asymptotic behavior of the vacuum averages is studied at the center of the sphere and near its surface. It is shown that for small values of the parameter describing the solid-angle deficit in the geometry of a global monopole, the vacuum stresses induced by the boundary are highly anisotropic.