Ground state energy of massive scalar field inside a spherical region in the global monopole background

Abstract

Using the zeta function regularization method we calculate the ground state energy of scalar massive field inside a spherical region in the space–time of a pointlike global monopole. Two cases are investigated: (i) First, we calculate the Casimir energy inside a sphere of radius R and analyze the obtained result. We observe that this energy may be positive or negative depending on metric coefficient α and nonconformal coupling ξ. In the limit R→∞, this energy vanishes: (ii) In the second model, we surround the monopole by an additional sphere of radius r0<R and consider the scalar field confined in the region between these two spheres. In this case, the ground state energy presents an additional contribution due to boundary at r0 which is divergent for small radius. Additional comments about renormalization are considered.