2025/03/21 by Semra Gürtaş Doğan, Abdullah Güvendi, Dogan, Semra Gurtas +3 · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Optics (physics.optics) #Quantum Electrodynamics and Casimir Effect
paper · pdf · doi:10.48550/arxiv.2503.18967
openalex publication_date 2025/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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(ρ,ω) is both spatially and spectrally dispersive, leading to a position-dependent critical frequency ωc(ρ) that delineates the boundary between propagating and evanescent modes. At high frequencies, the medium becomes asymptotically transparent, while for ω< ωc(ρ), 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.