Akademik Veri Yönetim Sistemi
Nuclear Physics B, cilt.1024, 2026 (SCI-Expanded, Scopus)
We investigate the propagation of a massless scalar field in the Gödel universe and demonstrate that the rotating spacetime functions as an intrinsically optically active medium, characterized by a refractive index that depends on both position and frequency. Starting from the covariant Klein-Gordon equation, we derive a generalized Helmholtz-type radial equation in which the effective refractive index n ∘(r, ω) explicitly depends on the radial coordinate r and frequency ω . Consequently, the Gödel geometry manifests as a rotation-induced optical medium: scalar modes are confined within a finite radial domain bounded by turning points where n∘2(r,ω)=0. Depending on the rotation rate Ω, the frequency ω , and the azimuthal quantum number m , the medium supports either propagating (n∘2'0) or evanescent (n∘2'0) behavior. Near the rotational axis, a centrifugal singularity emerges, producing strongly evanescent regions for | m | ' 1/2, whereas for m=0, propagation persists near the axis but confinement still occurs due to the evanescent asymptotics at large r . Asymptotically, n∘2(r→∞,ω)≃−3−Ω24ω2, rendering all modes evanescent. Planck-scale corrections are incorporated within the framework of rainbow gravity, employing energy-dependent functions f (ϵ) and g (ϵ), where ϵ=ω/ωp. We consider (i) loop-quantum-gravity-inspired functions f(ϵ)=1,g(ϵ)=1−ηϵ and (ii) doubly special relativity-inspired functions f(ϵ)=1/(1−ηϵ),g(ϵ)=1, which induce the frequency deformation ω→ω˜=ωf(ϵ)/g(ϵ) and lead to a modified refractive index n˜(r,ω,ωp). First-order corrections (η ϵ ≪ 1) yield analytic shifts of the turning points, while exact closed-form expressions allow precise numerical treatment. The resulting rainbow-induced deformations generate frequency-dependent modifications to the propagation thresholds, which become particularly pronounced near the axis (r → 0) and in near-Planckian regimes. Furthermore, we demonstrate that these results generalize to z -polarized electromagnetic wave modes and show the smooth recovery of scalar-like propagation in the Gödel universe. Finally, when η=0, we establish that in the high-frequency limit (ω → ∞), the effective refractive index accurately reproduces the null geodesics of the spacetime.