A brief introduction to Cadabra: a tool for tensor computations in General Relativity

TL;DR

Cadabra is a versatile computer algebra system tailored for tensor computations in General Relativity, facilitating routine calculations and verifications in high energy physics and gravitational research.

Contribution

This paper introduces Cadabra as a user-friendly tool for tensor algebra, demonstrating its application in key General Relativity computations.

Findings

Verified Levi-Civita connection as a metric connection

Derived the Gauss equation for curvatures

Showcased simple examples of tensor manipulations

Abstract

Cadabra is a powerful computer program for the manipulation of tensor equations. It was designed for use in high energy physics but its rich structure and ease of use lends itself well to the routine computations required in General Relativity. Here we will present a series of simple examples showing how Cadabra may be used, including verifying that the Levi-Civita connection is a metric connection and a derivation of the Gauss equation between induced and ambient curvatures.