Vacuum Polarization Effects on Flat Branes due to a Global Monopole

Abstract

In this paper we analyse the vacuum polarization effects associated with a massless scalar field in the higher-dimensional spacetime. Specifically we calculate the renormalized vacuum expectation value of the square of the field, $<{\Phi }^2(x){>}_{Ren}$, induced by a global monopole in the "braneworld" scenario. In this context the global monopole lives in a $n=3$ dimensional sub-manifold of the higher-dimensional (bulk) spacetime, and our Universe is represented by a transverse flat $(p-1)-$ dimensional brane. In order to develop this analysis we calculate the general Green function admitting that the scalar field propagates in the bulk. Also a general curvature coupling parameter between the field and the geometry is assumed. We explicitly show that the vacuum polarization effects depend crucially on the values attributed to $p$. We also investigate the general structure of the renormalized vacuum expectation value of the energy-momentum tensor, $<T_{\mu \nu }(x){>}_{Ren.}$, for $p=3$.

21 pages, 1 figure. Accepted for publication in PRD

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• Scalar self-energy for a charged particle in global monopole spacetime with a spherical boundary
• The deflection angle of a gravitational source with global monopole in the strong field limit
• Fermionic vacuum polarization by a composite topological defect in higher-dimensional space-time
• Vacuum polarization and classical self-action near higher-dimensional defects
• Vacuum polarization by a composite topological defect
• Induced self-energy on a static scalar charged particle in the spacetime of a global monopole with finite core
• Fermionic vacuum polarization in higher-dimensional global monopole spacetime
• Vacuum polarisation of Dirac fermions in the cosmological de Sitter-global monopole spacetime