Cadabra and Python algorithms in General Relativity and Cosmology I: Generalities

TL;DR

This paper demonstrates how the computer algebra system Cadabra can be effectively used to manipulate and analyze expressions in General Relativity and gravitational theories, highlighting its unique features and user-friendly packages.

Contribution

It introduces new functionalities and packages in Cadabra tailored for gravitational physics, emphasizing its distinct approach compared to other algebra systems.

Findings

Illustrates Cadabra's use in deriving field equations

Shows how to create user-defined packages in Cadabra

Provides examples of differential forms and solutions in gravity theories

Abstract

The aim of this work is to present a series of concrete examples which illustrate how the computer algebra system Cadabra can be used to manipulate expressions appearing in General Relativity and other gravitational theories. We highlight the way in which Cadabra's philosophy differs from other systems with related functionality. The use of various new built-in packages is discussed, and we show how such packages can also be created by end-users directly using the notebook interface. The current paper focuses on fairly generic applications in gravitational theories, including the use of differential forms, the derivation of field equations and the construction of their solutions. A follow-up paper discusses more specific applications related to the analysis of gravitational waves.