OGRePy: An Object-Oriented General Relativity Package for Python

Abstract

We present OGRePy, the official Python port of the popular Mathematica tensor calculus package OGRe (Object-Oriented General Relativity) - a powerful, yet user-friendly, tool for advanced tensor calculations in mathematics and physics, especially suitable for general relativity. The Python port uses the same robust and performance-oriented algorithms as the original package, and retains its core design principles. However, its truly object-oriented interface, enabled by Python, is more intuitive and flexible than the original Mathematica implementation. It utilizes SymPy for symbolic computations and Jupyter as a notebook interface. OGRePy allows calculating arbitrary tensor formulas using any combination of addition, multiplication by scalar, trace, contraction, partial derivative, covariant derivative, and permutation of indices. Transformations of the tensor components between different index configurations and/or coordinate systems are performed seamlessly behind the scenes as needed, eliminating user error due to combining incompatible representations, and guaranteeing consistent results. In addition, the package provides facilities for easily calculating various curvature tensors and geodesic equations in multiple representations. This paper presents the main features of the package in great detail, including many examples of its use in the context of general relativity research.