[论文解读] Wave Propagation and Effective Refraction in Lorentz-Violating Wormhole Geometries

Dogan, Semra Gurtas, Omar Mustafa+2 more|arXiv (Cornell University)|Feb 11, 2026

Noncommutative and Quantum Gravity Theories被引用 0

一句话总结

该论文发展了一种几何光学框架，用于研究在静态、球对称的 Lorentz 违背虫洞时空中无质量标量波，推导出与位置和频率相关的有效折射率，并分析回转点与地平线。

ABSTRACT

We study the propagation of massless scalar waves in static, spherically symmetric Lorentz-violating wormhole spacetimes within a geometric-optical framework. Starting from a general metric characterized by an arbitrary lapse function and areal radius, we derive curvature invariants, establish regularity conditions at the wormhole throat, and reduce the Klein-Gordon equation to a Helmholtz-type radial wave equation. This formulation naturally leads to a position- and frequency-dependent effective refractive index determined by the underlying spacetime geometry and Lorentz-violating structure, resulting in effective frequency-dependent wave-optical behavior. We show that divergences of the refractive index coincide with Killing horizons, while curvature-induced turning points control reflection, transmission, and confinement of scalar waves. By analyzing constant, linear, and quadratic lapse profiles, we identify horizonless transmission regimes, asymmetric wave propagation, and multi-horizon trapping structures. Our results reveal that Lorentz violation can significantly modify wave-optical properties of curved spacetime, generating graded-index analogues and geometric confinement of modes without curvature singularities. This unified optical perspective provides a robust framework for investigating wave scattering, resonances, and potential observational signatures in Lorentz-violating gravitational backgrounds.

研究动机与目标

• Motivate the study of wave propagation in Lorentz-violating wormhole geometries as a probe of underlying spacetime structure.
• Formulate a general static, spherically symmetric wormhole metric with arbitrary lapse function A(x) and areal radius r(x).
• Derive curvature invariants and throat regularity conditions to characterize the geometry.
• Reduce the Klein-Gordon equation to a one-dimensional radial equation with an effective potential.
• Establish an optical analogy where geometry induces a frequency-dependent refractive index and analyze its implications for wave propagation.

提出的方法

• Define the metric ds^2 = -A(x) dt^2 + (1/A(x)) dx^2 + r(x)^2(dθ^2 + sin^2θ dφ^2) and compute Christoffel symbols.
• Reduce the massless Klein-Gordon equation to a radial equation for R(x) and transform R(x) = ψ(x)/(r(x)√A(x)) to obtain a Schrödinger-like form ψ'' + [ω^2/A^2 - V0(x)] ψ = 0.
• Identify an effective wavenumber k_eff^2 = ω^2 n(ω,x)^2 and define the geometry-induced refractive index n(ω,x) from the Helmholtz-type reformulation.
• Analyze the refractive-index divergences and turning points to interpret horizons and propagation barriers.
• Explore constant, linear, and quadratic lapse profiles to illustrate horizonless transmission, asymmetry, and multi-horizon trapping.

Figure 1: Plots of $n(\omega,x)^{2}$ versus $x$ for $\ell=a=1$ and different Lorentz-violating parameters $\eta=0,2/3,0.9$ at $\omega=1,2,4$ . Table 1 reports the corresponding turning point locations.

实验结果

研究问题

• RQ1 How does Lorentz-violating gravity modify the wave propagation of massless scalar fields in wormhole spacetimes?
• RQ2 Can curvature alone induce an optical-like refractive index and turning-point structure in vacuum?
• RQ3 What is the relationship between Killing horizons, refractive-index singularities, and wave propagation regimes?
• RQ4 How do different lapse profiles (constant, linear, quadratic) affect transmission, reflection, and confinement of scalar waves?

主要发现

• A geometry-induced, frequency-dependent effective refractive index arises from the background metric and Lorentz-violating structure, governing wave propagation.
• Divergences of the refractive index coincide with Killing horizons, not curvature singularities, marking breakdowns of static optical description rather than true pathologies.
• Turning points defined by n(ω,x)^2 = 0 separate propagating and evanescent regions, controlling reflection, transmission, and confinement.
• Constant lapse (horizonless) wormholes can display turning points that depend on frequency and Lorentz-violating parameter, affecting transmission windows.
• Linear lapse introduces a single Killing horizon and produces directional asymmetry in wave propagation, akin to graded-index media.
• Quadratic lapse with two Killing horizons can confine waves and support trapped or quasi-bound modes, illustrating global geometric confinement without curvature singularities.

Figure 2: Plots of $n(\omega,x)^{2}$ versus $x$ for $\ell=a=1$ , $\eta=2/3$ , and $\omega=1,2,4$ , for different Rindler-type acceleration values $\chi=0.02,0.2,1$ . Table 2 reports the corresponding turning points and Killing horizon locations.