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arXiv:2607.23331

Effects of Curvature-Scalar Coupling on Vacuum Energy in Flat (3+1)-Dimensional Space-Time

Volodymyr Gorkavenko, Oleh Barabash, Pavlo Nakaznyi, Mariia Tsarenkova, Nazar Yakovenko, Andrii Zaporozhchenko

hep-thmath-phquant-phSubmitted Jul 25, 2026• Announced Jul 28, 2026
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Abstract

We investigated how a magnetic topological defect affects the vacuum polarization of a charged massive scalar field in a flat $(3+1)$-dimensional space-time. The defect was modeled as an impenetrable to matter field finite-thickness tube with magnetic flux inside. We implemented the most general form of the Robin boundary condition on the surface of the magnetic tube, which enables a fully general analysis of the problem. We have found that in flat spacetime, the total vacuum energy generated by a magnetic topological defect depends on the curvature $ξ$, except for special cases corresponding to the Dirichlet and Neumann boundary conditions. By contrast, when Robin's general boundary conditions are imposed, the induced vacuum energy acquires an explicit dependence on the curvature coupling $ξ$, which is significant even in flat space-time. A detailed study of the dependence of the effect on the boundary condition parameter has been carried out. The obtained results highlight the nontrivial role played by boundary conditions in vacuum polarization phenomena.

Journal reference
Universe 12.2, p.47 (2026)
DOI
10.3390/universe12020047
Comments
12 pages, 3 figures

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We investigated how a magnetic topological defect affects the vacuum polarization of a charged massive scalar field in a flat (3+1)(3+1)(3+1)-dimensional space-time. The defect was modeled as an impenetrable to matter field finite-thickness tube with magnetic flux inside. We implemented the most general form of the Robin boundary condition on the surface of the magnetic tube, which enables a fully general analysis of the problem. We have found that in flat spacetime, the total vacuum energy generated by a magnetic topological defect depends on the curvature ξξξ, except for special cases corresponding to the Dirichlet and Neumann boundary conditions. By contrast, when Robin's general boundary conditions are imposed, the induced vacuum energy acquires an explicit dependence on the curvature coupling ξξξ, which is significant even in flat space-time. A detailed study of the dependence of the effect on the boundary condition parameter has been carried out. The obtained results highlight the nontrivial role played by boundary conditions in vacuum polarization phenomena.
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We develop a general framework for investigating the influence of topological defects on the local characteristics of a quantum scalar field in a warped geometry background. The Ricci tensor and curvature scalar are decomposed into contributions from the warp factor, the radial geometry and the angular defect structure. For an arbitrary curvature coupling parameter, the field equation is separated into independent radial, angular and warp-coordinate parts. A complete set of normalized mode functions is obtained for general values of the angular deficit parameters. The general formalism is applied to several specific cases, such as conformally flat warped spacetimes, generalized cosmic strings, global monopoles and anti-de Sitter (AdS)-type warped geometries. The Hadamard two-point function is then evaluated for a global monopole in AdS spacetime using the obtained mode functions.