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arXiv:2607.09997

Scalar and vector bosons in a Bonnor-Melvin-$Λ$ spacetime: an exact Duffin-Kemmer-Petiau analysis

Francisco A. Cruz Neto, Luis B. Castro

gr-qchep-thmath-phquant-phSubmitted Jul 10, 2026• Announced Jul 14, 2026
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Abstract

We study scalar and vector bosons in the Bonnor--Melvin--$Λ$ spacetime within the Duffin--Kemmer--Petiau (DKP) formalism. By employing Umezawa's projection operators, we separate the physical spin-0 and spin-1 sectors and derive the corresponding exact second-order equations in the full curved spacetime, without relying on the conical approximation. For the scalar sector, the radial equation reduces to a Schrödinger-like equation with a trigonometric Pöschl--Teller effective potential. In the vector sector, the longitudinal mode is governed by the same effective potential, whereas the transverse polarizations are described by generalized trigonometric Pöschl--Teller potentials. Because the me\-tric function vanishes at a discrete set of radial points, the radial dynamics is naturally formulated as a singular Sturm--Liouville problem on a fundamental interval, with the physical radial domain fixed by the Friedrichs self-adjoint extension of the corresponding singular radial operators. As a result, all physical sectors exhibit purely discrete radial spectra, and their eigenfunctions are obtained in closed form. These results provide a unified exact treatment of scalar and vector bosons in the Bonnor--Melvin--$Λ$ spacetime, complement previous analyses based on the conical approximation, and clarify the role of the global geometric structure of the background in shaping confinement and spectral properties.

Journal reference
Eur. Phys. J. C 86 (2026) 902
DOI
10.1140/epjc/s10052-026-16118-9
Comments
20 pages, 4 figures

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