发表机构
China West Normal University; Chongqing Normal University; Fuyang University of Technology; Universidade Federal de Campina Grande; Instituto de Física, Universidade de São Paulo（西华师范大学; 重庆师范大学; 阜阳理工学院; 坎皮纳格兰德联邦大学; 圣保罗大学物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过测地线边界值问题和惠更斯-菲涅耳构造，将RN黑洞电荷依赖几何映射为类比表面的相干波响应，揭示电荷统一控制路径谱并支配宏观干涉现象，为类比引力实验提供可调蓝图。
AI 中文摘要
为了揭示相对论致密天体的内禀度规如何支配宏观波动现象，我们建立了一个理论框架，将Reissner-Nordström（RN）黑洞的电荷依赖空间几何映射到类比弯曲表面的相干响应上。通过在等距嵌入的赤道切片上求解精确的空间测地线边值问题，我们提取了离散的多环路径长度谱，并通过有限路径表面惠更斯-菲涅耳构造将该几何骨架转换为物理波场。我们解析计算了任意阶绕行轨迹及其高绕行累积极限，表明类比电荷充当精确的物理旋钮，可重构事件视界喉部并从根本上重组离散路径序列。此外，我们发现这一潜在的几何形变唯一地决定了宏观干涉，揭示了稳态空间条纹、光谱共振梳和瞬态时间回波阶梯本质上是由单一电荷控制的路径谱所统一投射的物理现象。这种从系统参数到响应的系统方法在强场引力透镜与桌面变换光学之间建立了严格的理论桥梁，为未来多领域类比引力实验提供了高度可调的蓝图。
英文摘要
To uncover how the intrinsic metric of a relativistic compact object governs macroscopic wave phenomena, we establish a theoretical framework mapping the charge dependent spatial geometry of a Reissner-Nordström (RN) black hole onto the coherent response of an analogue curved surface. By solving an exact spatial geodesic boundary value problem on an isometrically embedded equatorial slice, we extract the discrete multi-loop path-length spectrum and convert this geometric backbone into a physical wave field via a finite-path surface Huygens-Fresnel construction. We analytically compute the arbitrary order winding trajectories alongside their high winding accumulation limits, demonstrating that the analogue charge acts as a precise physical dial that reconfigures the event horizon throat and fundamentally reorganizes the discrete path sequence. Furthermore, we find that this underlying geometric deformation uniquely dictates the macroscopic interference, revealing that steady state spatial fringes, spectral resonance combs, and transient temporal echo ladders are intrinsically unified physical projections of a single charge controlled path spectrum. This systematic parameter to response methodology establishes a rigorous theoretical bridge between strong field gravitational lensing and tabletop transformation optics, providing a highly tunable blueprint for future multi domain analogue gravity experiments.
Comments25 pages, 9 figures
