OGRe: An Object-Oriented General Relativity Package for Mathematica

TL;DR

OGRe is a user-friendly, object-oriented Mathematica package that simplifies complex tensor calculations in general relativity by automating transformations, error prevention, and providing advanced features for tensor manipulation.

Contribution

It introduces an object-oriented design to tensor calculus in Mathematica, enabling easier, more reliable calculations specifically tailored for general relativity applications.

Findings

Automates tensor transformations and index management

Prevents user errors in tensor operations

Includes features like curvature tensor calculation and geodesic equations

Abstract

We present OGRe, a modern Mathematica package for tensor calculus, designed to be both powerful and user-friendly. The package can be used in a variety of contexts where tensor calculations are needed, in both mathematics and physics, but it is especially suitable for general relativity. By implementing an object-oriented design paradigm, OGRe allows calculating arbitrarily complicated tensor formulas easily, and automatically transforms between index configurations and coordinate systems behind the scenes as needed, eliminating user errors by making it impossible for the user to combine tensors in inconsistent ways. Other features include displaying tensors in various forms, automatic calculation of curvature tensors and geodesic equations, easy importing and exporting of tensors between sessions, optimized algorithms and parallelization for improved performance, and more.