Using Maple and GRTensorIII in relativistic spherical models

TL;DR

This paper demonstrates how Maple and GRTensorIII can be effectively used to analyze and simplify algebraic expressions in relativistic spherical models, aiding in the search for exact solutions of Einstein's equations.

Contribution

It introduces algebraic programming procedures in Maple with GRTensorIII for studying spherical symmetry and finding solutions to Einstein's field equations.

Findings

Effective use of Maple and GRTensorIII for algebraic manipulation in relativity

Simplification procedures for Einstein field equations with spherical symmetry

Facilitation of exact solution search in relativistic models

Abstract

This article presents some aspects and experience in the use of algebraic manipulation software applied to general relativity. Some years ago certain results were reported using computer algebra platforms, but the growing popularity of graphical platforms such as Maple allows us to approach the problem of the simplifications of many expressions from another point of view. Some simple algebraic programming procedures are presented (in Maple with the GrTensorIII package) to obtain and study material distributions with spherical symmetry and to search for exact solutions of the Einstein field equations. The purpose is to show how useful a computer algebra system can be. All calculations were performed using the GRTensorIII computer algebra package, which runs on Maple 2017, along with several Maple routines that we have used specifically for the simplification of many of the algebraic expressions that are very common in this type of problem.