AI 中文总结
该研究分析广义相对论中由内禀空间应变产生的时空捷径，证明超静态走廊可实现旅行时间提前，并给出因果与源约束条件。
AI 中文摘要
我们分析了在固定参考体积下，由内禀空间度规的纵向收缩和横向膨胀所产生的时空捷径。光滑有界的超静态走廊是全局双曲且测地完备的，并在外部时钟之间产生精确的旅行时间提前。轴向最大值使轴向光线成为全局最短线；内部区间上的严格最大值建立了奥勒姆关于精确匹配走廊的端点表面判据。精确的爱因斯坦源恒等式将积分欧拉物质能量与渐近质量区分开来：无限长管道具有负的积分能量，而有限走廊则允许竞争的梯度贡献。横向里奇恒等式证明了在每个非平凡的局部化有限走廊中，局部零能量条件被违反。对于局部化轴向最大值轮廓，轴向平均零能量严格为负，并且定量界限将其大小与参考时间提前和峰值应变联系起来。我们还获得了完整的有限轮廓里奇谱和轴向乘客潮汐张量。这些结果为制备的几何结构提供了明确的因果和源约束，而无需指定其物理形成或物质动力学。
英文摘要
We analyze spacetime shortcuts generated by longitudinal contraction and transverse expansion of the intrinsic spatial metric at fixed reference volume. Smooth bounded ultrastatic corridors are globally hyperbolic and geodesically complete and produce an exact travel-time advance between exterior clocks. An axial maximum makes the axial light ray globally minimizing; a strict maximum on an interior interval establishes Olum's endpoint-surface criterion for exactly matched corridors. Exact Einstein-source identities distinguish integrated Eulerian matter energy from asymptotic mass: infinite tubes have negative integrated energy, whereas finite corridors admit competing gradient contributions. A transverse Ricci identity proves local null-energy violation in every nontrivial localized finite corridor. The axial averaged null energy is strictly negative for localized axial-maximum profiles, and quantitative bounds relate its magnitude to the reference time advance and peak strain. We also obtain the complete finite-profile Ricci spectrum and the axial passenger tidal tensor. These results provide explicit causal and source constraints on a prepared geometry without specifying its physical formation or matter dynamics.
Comments15 pages, 4 figures
