Photon rings in three-dimensional Bonnor-Melvin magnetic spacetime

Abstract

We present a rigorous analysis of the relativistic dynamics of vector bosons propagating in a (2 + 1)-dimensional Bonnor-Melvin magnetic spacetime, characterized by an out-of-plane aligned magnetic field and a nonzero cosmological constant Lambda. To achieve this, we derive the exact solution of the fully covariant vector boson equation corresponding to the spin-1 sector of the Duffin-Kemmer-Petiau equation in 2 + 1 dimensions. The magnetic background arises naturally as the 2 + 1 + 0-brane configuration within the Bonnor-Melvin solution to gravity coupled with nonlinear electrodynamics. By deriving the radial wave equation that is mathematically equivalent to the Helmholtz equation governing massless vector bosons, we obtain exact eigenvalue spectra applicable to both massive and massless vector bosons (photons). Remarkably, our results reveal that photons exhibit a finite, nonzero ground-state energy, with their quantum states manifesting solely as rotating ring-like modes.