标题： PyGRO：一种用于广义相对论轨道的Python积分器 显示英文标题

标题： PyGRO: a Python Integrator for General Relativistic Orbits

摘要： 近年来实验引力领域的进展使得在以前未探索的领域中测试等效原理成为可能，从而实现了对广义相对论前所未有的验证，并且也使对替代引力理论的测试成为可能。 我们引入了一种新的计算工具 PyGRO，旨在对任何解析四维时空中的大质量及无质量测试粒子轨迹的测地线方程进行数值积分。 结果是一个现代、快速、开源、高度可定制且用户友好的 Python 包，用于执行测地线方程的数值积分。 结合符号和数值计算，PyGRO 提供了多种方法，以最少的用户干预获得完全相对论轨道，在任何用户给定的时空度规张量的符号表达式下都能通用。 我们在一系列不同的场景中测试了 PyGRO，通过成功重现广义相对论的经典结果来验证所采用的方法，这些结果我们在本文中进行了报告。 显示英文摘要

摘要： Advancement in recent years in the field of experimental gravitation has allowed to test the equivalence principle in regimes that were previously unexplored, allowing for unprecedented verifications of general relativity and also enabling tests of alternative theories of gravity. We introduce a new computational tool, PyGRO, with the aim of integrating numerically the geodesic equations for the trajectories of massive and massless test particles in any analytic four-dimensional space-time. The result is a modern, fast, open-source, highly customizable and user-friendly Python package to perform the numerical integration of the the geodesic equations. Combining symbolic and numerical calculations, PyGRO offers a variety of methods to obtain fully relativistic orbits with minimal intervention by the user, working in full generality with any user-given symbolic expression of the space-time metric tensor. We have tested PyGRO in an array of different scenarios, validating the methodology employed by successfully reproducing classical results from general relativity, which we report in this article.