Dündar, F S.Kelekçi, Ö.Ayar, Gülhan2026-01-102026-01-102024https://doi.org/10.1002/mma.10589https://hdl.handle.net/20.500.12684/22171In recent years, numerous studies have appeared that considered Killing vectors of three-dimensional Riemannian manifolds as magnetic fields, since these vector fields are divergenceless by definition. The existence of adivergenceless vector field modeled as a magnetic field does not imply that it is physically realizable. In this study, we propose a physical classification scheme based on the divergences of the integral that defines the energy of a Killing magnetic field. We consider all the Killing magnetic fields of Thurston geometries studied in the literature and classify them as either physical or nonphysical.en10.1002/mma.10589info:eu-repo/semantics/closedAccessKilling magnetic fieldsphysical classificationThurston geometriesArticle44850165023