Using Cadabra for tensor computations in General Relativity

TL;DR

This paper introduces Cadabra, a user-friendly open-source tool that simplifies complex tensor calculations in General Relativity, demonstrated through tutorials and practical examples.

Contribution

It provides a comprehensive tutorial and source code for using Cadabra to perform tensor computations in General Relativity, including derivations of key equations.

Findings

Cadabra effectively handles tensor algebra in GR.

The tutorial covers from basic syntax to complex derivations.

Source code and exercises are publicly available on GitHub.

Abstract

Cadabra is an open access program ideally suited to complex tensor commutations in General Relativity. Tensor expressions are written in LaTeX while an enhanced version of Python is used to control the computations. This tutorial assumes no prior knowledge of Cadabra. It consists of a series of examples covering a range of topics from basic syntax such as declarations, functions, program control, component computations, input and output through to complete computations including a derivation of two of the BSSN equations from the ADM equations. Numerous exercises are included along with complete solutions. All of the source code for the examples, exercises and solutions are available on GitHub.