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arXiv · 2609.22860

Charged Klein-Gordon modes on an Ellis wormhole: magnetic confinement and conditional Heun solvability

Abdullah Guvendi·Omar Mustafa
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Abstract

We study charged Klein-Gordon modes on a $(2+1)$-dimensional Ellis traversable wormhole in an external magnetic field defined as uniform in an auxiliary Euclidean embedding space. The spatial geometry is intrinsically catenoidal, while the embedding is used only to construct the external gauge connection. Pullback of the ambient potential yields a regular azimuthal gauge field whose associated intrinsic magnetic scalar reverses sign across the throat. Separation of the Klein-Gordon equation leads to a radial problem that is unitarily equivalent to a one-dimensional Schrödinger operator with a regular effective potential. For nonzero magnetic coupling, the quadratic asymptotic term produces radial confinement on the complete wormhole. The radial equation can be reduced to the confluent-Heun class. Polynomial truncation is possible only on constrained parameter submanifolds determined by simultaneous termination conditions and therefore does not represent the generic confined spectrum. We derive the corresponding relativistic energies and analyze the lowest polynomial sector, while distinguishing the formal continuous-$\ell$ solvability correlations from the integer values of the azimuthal separation constant required by the standard angular periodicity condition.

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Abdullah Guvendi, Omar Mustafa. 2026-09-19. Charged Klein-Gordon modes on an Ellis wormhole: magnetic confinement and conditional Heun solvability. https://arxiv.org/abs/2609.22860

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