Geometric and wave optics in a BTZ optical metric-based wormhole

---

Gürtaş Doğan S., Güvendi A., Mustafa O.

Physics Letters B, cilt.868, ss.139824, 2025 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 868
• Basım Tarihi: 2025
• Doi Numarası: 10.1016/j.physletb.2025.139824
• Dergi Adı: Physics Letters B
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
• Sayfa Sayıları: ss.139824
• Hakkari Üniversitesi Adresli: Evet

Özet

We investigate the geometric and wave optical properties of a (2+1)-dimensional ultra-static spacetime conformally related to the static BTZ black hole, characterized by constant negative Gaussian curvature. The associated optical metric defines a hyperbolic wormhole geometry, wherein null geodesics experience a Pöschl–Teller-type repulsive effective potential that suppresses circular photon orbits and directs all trajectories toward the optical origin. In the wave regime, we reformulate the Helmholtz equation into a Schrödinger-like form, revealing a spatially localized effective potential that encodes curvature and angular momentum effects. The resulting refractive index $n(\rho,\omega)$ is both spatially and spectrally dispersive, leading to a position-dependent critical frequency $\omega_c(\rho)$ that delineates the boundary between propagating and evanescent modes. At high frequencies, the medium becomes asymptotically transparent, while for $\omega < \omega_c(\rho)$, waves undergo exponential attenuation. These results demonstrate intrinsic curvature-induced spectral filtering and provide a geometrically tunable framework for analog gravity systems and graphene-based photonic platforms.