We present a numerical weak-lensing analysis that is fully relativistic and non-perturbative for the scalar part of the gravitational potential and first-order in the vector part, frame dragging. Integrating the photon geodesics backwards from the observer to the emitters, we solve the Sachs optical equations and study in detail the weak-lensing convergence, ellipticity and rotation. For the first time, we apply such an analysis to a high-resolution relativistic N-body simulation, which consistently includes the leading-order corrections due to general relativity on both large and small scales. These are related to the question of gauge choice and to post-Newtonian corrections, respectively. We present the angular power spectra and one-point probability distribution functions for the weak-lensing variables, which we find are broadly in agreement with comparable Newtonian simulations. Our geometric approach, however, is more robust and flexible, and can therefore be applied consistently to non-standard cosmologies and modified theories of gravity.

中文翻译：

---

相对论 N 体模拟中的弱透镜观测

我们提出了一种数值弱透镜分析，对于引力势的标量部分和矢量部分的一阶，框架拖动，它是完全相对论的和非微扰的。将光子测地线从观察者向后集成到发射器，我们求解 Sachs 光学方程并详细研究弱透镜会聚、椭圆度和旋转。我们第一次将这样的分析应用于高分辨率的相对论 N 体模拟，该模拟始终包括由于广义相对论在大尺度和小尺度上的超前阶修正。这些分别与规范选择问题和后牛顿修正有关。我们给出了弱透镜变量的角功率谱和单点概率分布函数，我们发现这与可比较的牛顿模拟大体一致。然而，我们的几何方法更加稳健和灵活，因此可以一致地应用于非标准宇宙学和修正的引力理论。