Ground State Energy of Massive Scalar Field Inside a Spherical Region in the Global Monopole Background

TL;DR

This paper calculates the ground state energy of a massive scalar field inside a spherical region around a global monopole using zeta function regularization, analyzing effects of geometry, boundary conditions, and coupling.

Contribution

It provides an analytical calculation of Casimir energy in a global monopole background, including boundary effects and divergence analysis, which is novel in this context.

Findings

Casimir energy can be positive or negative depending on parameters

Zero energy result in the limit of infinite sphere radius

Additional boundary introduces divergent contributions for small radii

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 point-like global monopole. Two cases are investigated: (i) We calculate the Casimir energy inside a sphere of radius $R$ and make an analytical analysis about it. We observe that this energy may be positive or negative depending on metric coefficient $\alpha$ and non-conformal coupling $\xi$. In the limit $R\to\infty$ we found a zero result. (ii) In the second model we surround the monopole by additional sphere of radius $r_0<R$ and consider scalar field confined in the region between these two spheres. In the latter, the ground state energy presents an additional contribution due to boundary at $r_0$ which is divergent for small radius. Additional comments about renormalization are considered.