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 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.

30 pages and 2 figures. LATEX file

References in corpus (1)

• Zeta Functions and the Casimir Energy

Cited by in corpus (15)

• Heat kernel expansion: user's manual
• Casimir effect in a wormhole spacetime
• Ground state energy in a wormhole space-time
• Spinor Casimir densities for a spherical shell in the global monopole spacetime
• Spinor Casimir effect for concentric spherical shells in the global monopole spacetime
• Polarization of the fermionic vacuum by a global monopole with finite core
• Semiclassical wormholes
• Casimir densities for two concentric spherical shells in the global monopole spacetime
• Casimir densities for a spherical shell in the global monopole background
• Vacuum Polarization Effects on Flat Branes due to a Global Monopole
• Vacuum polarization by a global monopole with finite core
• Casimir energy for spherical shell in Schwarzchild black hole background
• Vacuum polarization by a scalar field in de Sitter spacetime in the presence of global monopole
• Casimir densities for parallel plate in the Domain Wall background
• Spherical Casimir effect for a massive scalar field on the three dimensional ball