We introduce a new, open-source computational general relativity framework for the Wolfram Language called Gravitas, which boasts a number of novel and distinctive features as compared to the many pre-existing computational and numerical relativity frameworks currently available within the open-source community. These include, but are not limited to: seamless integration of its powerful symbolic and numerical subsystems, and, by extension, seamless transition between analytic/continuous representations and numerical/discrete representations of arbitrary spacetime geometries; highly modular, general and extensible representations of spacetime geometries, spacetime topologies, gauge conditions, coordinate systems, matter fields, evolution equations and initial data; ability to set up and run complex numerical relativity simulations, and to perform 2D and 3D visualizations, symbolic computations and numerical analysis (including the extraction of gravitational wave signals) on the resulting data, all from within a single notebook environment; and a totally-unstructured adaptive refinement scheme based on hypergraph rewriting, allowing for exceedingly efficient discretization and numerical evolution of Cauchy initial data for a wide range of challenging computational problems involving strong relativistic field dynamics. In this first in a series of two articles covering the framework, we focus on the design and capabilities of Gravitas's symbolic subsystem, including its general and flexible handling of arbitrary geometries parametrized by arbitrary curvilinear coordinate systems (along with an in-built library of standard metrics and coordinate conditions), as well as its various high-level tensor calculus and differential geometry features. We proceed to show how this subsystem can be used to solve the Einstein field equations both analytically and numerically.

翻译：我们介绍一个用于 Wolfram 语言的开源计算广义相对论新框架 Gravitas，与现有开源社区中众多计算和数值相对论框架相比，该框架具备若干新颖且独特的特性。这些特性包括但不限于：其强大的符号子系统和数值子系统的无缝集成，进而实现任意时空几何的解析/连续表示与数值/离散表示之间的平滑过渡；时空几何、时空拓扑、规范条件、坐标系、物质场、演化方程及初始数据的高度模块化、通用且可扩展表示；能够设置并运行复杂的数值相对论模拟，并在单个笔记本环境中对所得数据进行二维和三维可视化、符号计算及数值分析（包括引力波信号提取）；以及基于超图重写的完全非结构化自适应细化方案，可针对涉及强相对论场动力学的各类挑战性计算问题，实现柯西初始数据极其高效的离散化和数值演化。在本系列两篇文章中的第一篇中，我们聚焦于 Gravitas 符号子系统的设计与能力，包括其对任意曲线坐标系参数化的任意几何的通用灵活处理（以及内置的标准度规和坐标条件库），及其多种高阶张量微积分和微分几何特性。我们进而展示如何利用该子系统解析和数值求解爱因斯坦场方程。