标题： 关于全局高斯弯曲测度及其在定态时空中的应用 显示英文标题

标题： On the global Gaussian bending measure and its applications in stationary spacetimes

摘要： 修正引力理论被提出以解决广义相对论的局限性，每种理论在强场极限下表现出差异。 然而，目前缺乏有效的手段通过局部强场测量来区分或检验这些理论。 在这项工作中，我们在奇异时空区域上定义了一个全局高斯弯曲测度，建立了相应的全局理论，并展示了它在一般静态时空中的应用。 该全局理论基于微分几何，而非特定的引力理论，因此可以在广义相对论及其之外描述各种物理现象。 例如，它可以用于描述无质量或有质量信使的引力弯曲，如光子、中微子、宇宙射线以及某些引力理论预测的可能有质量的引力波。 此外，该全局理论适用于任何旋转黑洞外部的静态时空区域。 作为其直接应用的一个实例，我们研究了黑洞在其周围区域内的高度弯曲时空效应，并设计了涉及不同形状的奇异透镜补丁的局部强场实验。 因此，可以预期根据该全局理论开发出新的方法，以区分不同的引力理论并在其强场区域对其进行测试。 显示英文摘要

摘要： Modified gravity theories have been suggested to address the limitations of general relativity, each exhibiting differences, particularly in their strong-field limits. Nonetheless, there lacks effective means to distinguish or test these theories through local strong-field measurements. In this work, we define a global Gaussian bending measure over singular spacetime regions, establish a corresponding global theory, and demonstrate its applications in a general stationary spacetime. The global theory is based on differential geometry, rather than on specific gravity theories, allowing it to depict various physics within general relativity and beyond. For example, it can be applied to describe the gravitational bending of massless or massive messengers, such as photons, neutrinos, cosmic rays, and possibly massive gravitational waves predicted in certain theories of gravity. Besides, the global theory is applicable to any stationary spacetime regions outside a rotating black hole. As an instance of its direct applications, we investigate the highly-curved spacetime effects of the black hole in its immediate surrounding regions and design local strong-field experiments involving different shapes of singular lensing patches. New means can be therefore anticipated to be developed according to the global theory to differentiate between different gravity theories and test them in their strong-field regions.