Geometric and wave optics in a BTZ optical metric-based wormhole
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| Format: | Preprint |
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2025
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| _version_ | 1866909734181797888 |
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| author | Dogan, Semra Gurtas Guvendi, Abdullah Mustafa, Omar |
| author_facet | Dogan, Semra Gurtas Guvendi, Abdullah Mustafa, Omar |
| contents | 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 $ω_c(ρ)$ that delineates the boundary between propagating and evanescent modes. At high frequencies, the medium becomes asymptotically transparent, while for $ω< ω_c(ρ)$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_18967 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric and wave optics in a BTZ optical metric-based wormhole Dogan, Semra Gurtas Guvendi, Abdullah Mustafa, Omar General Relativity and Quantum Cosmology Optics 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 $ω_c(ρ)$ that delineates the boundary between propagating and evanescent modes. At high frequencies, the medium becomes asymptotically transparent, while for $ω< ω_c(ρ)$, 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. |
| title | Geometric and wave optics in a BTZ optical metric-based wormhole |
| topic | General Relativity and Quantum Cosmology Optics |
| url | https://arxiv.org/abs/2503.18967 |