AI 中文总结
研究爱因斯坦 - 罗森引力波非对易形变中测试粒子动力学，通过考虑径向与轴向坐标非对易结构微扰研究粒子运动，发现形变产生耦合，非对易效应增强对引力构型紫外结构敏感性，分析了不同波的情况并导出相关解析表达式。
AI 中文摘要
我们在由柴奇安等人发展的非对易曲面黎曼几何框架内，研究爱因斯坦 - 罗森引力波非对易形变所引发的现象学效应。考虑径向与轴向坐标间的非对易结构，微扰地研究相应形变几何中非相对论测试粒子的运动。结果表明，形变在径向和纵向扇区间产生耦合，在考虑的微扰阶次下，径向动力学不受非对易形变影响。诱导的纵向响应由引力波轮廓的谱加权泛函支配，意味着纵向可观测量比其对易径向对应物依赖更高阶谱矩。因此，非对易效应展现出对引力构型紫外结构的增强敏感性。我们分别分析了单色爱因斯坦 - 罗森波和局域化的韦伯 - 惠勒脉冲。在单色情形下，非对易修正诱导出准周期纵向运动，而对于韦伯 - 惠勒脉冲，它产生类似于引力速度记忆效应的脉冲纵向响应。此外，我们在对易广义相对论中导出了在微扰区域大径向距离处由韦伯 - 惠勒脉冲产生的残余径向速度的显式解析表达式。
英文摘要
We investigate phenomenological effects induced by a noncommutative deformation of Einstein--Rosen gravitational-waves within the framework of the Riemannian geometry of noncommutative surfaces developed by Chaichian et al. Considering a noncommutative structure between the radial and axial coordinates, we study perturbatively the motion of nonrelativistic test particles in the corresponding deformed geometry. We show that the deformation generates a coupling between the radial and longitudinal sectors, while the radial dynamics remains unaffected by the noncommutative deformation at the perturbative order considered. The induced longitudinal response is governed by a spectrally weighted functional of the gravitational-wave profile, implying that longitudinal observables depend on higher-order spectral moments than their commutative radial counterparts. As a consequence, noncommutative effects exhibit enhanced sensitivity to the ultraviolet structure of the gravitational configuration. We analyze separately monochromatic Einstein--Rosen waves and the localized Weber--Wheeler pulse. In the monochromatic case, the noncommutative correction induces a quasi-periodic longitudinal motion, whereas for the Weber--Wheeler pulse it produces an impulsive longitudinal response analogous to a gravitational velocity memory effect. In addition, we derive an explicit analytical expression in commutative General Relativity for the residual radial velocity generated by the Weber--Wheeler pulse at large radial distances in the perturbative regime.
