The use of the algebraic programming in teaching general relativity

This is a review devoted to some results of Algebraic Programming (Computer Algebra) used in treating several problems of general relativity, based mainly on already published articles. The article contains the talk given by the author at The Albert Einstein Institut, Max Planck Institut fur Gravitationstheorie, Golm, Germany, september 2000

We survey the application of computer algebra in the context of gravitational theories. After some general remarks, we show of how to check the second Bianchi-identity by means of the Reduce package Excalc. Subsequently we list some computer algebra systems and packages relevant to applications in gravitational physics. We conclude by presenting a couple of typical examples.

In this paper we present our recent work in developing a computer-algebra tool for systems of partial differential equations (PDEs), termed "Kranc". Our work is motivated by the problem of finding solutions of the Einstein equations through numerical simulations. Kranc consists of Mathematica based computer-algebra packages, that facilitate the task of dealing with symbolic tensorial calculations and realize the conversion of systems of partial differential evolution equation...

Algebraic computing in relativity and gravitation dates back more than thirty years, but only relatively recently has hardware of sufficient power to tackle large scale calculations become commonplace. Whereas it is generally understood throughout the relativity community that there are a number of packages available, the diversity of problems that the available packages can help with is not so widely appreciated. This session was devoted to computer algebra for relativity an...

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 obt...

This Resource Letter provides some guidance on issues that arise in teaching general relativity at both the undergraduate and graduate levels. Particular emphasis is placed on strategies for presenting the mathematical material needed for the formulation of general relativity.

A brief characteristic of the specialized computer algebra system GRG_EC intended for symbolic computations in the field of general relativity is given.

We give a pedagogical introduction of the essential features of General Theory of Relativity (GTR) in the format of an undergraduate (UG) project. A set of simple MATHEMATICA code is developed which enables the UG students to calculate the tensorial objects without prior knowledge of any package operation. The orbit equations of light and material particle in Minkowski and Schwarzschild spacetime are solved numerically to illustrate the crucial tests of GTR.

Computer algebra programs are presented for application in general relativity, in electrodynamics, and in gauge theories of gravity. The mathematical formalism used is the calculus of exterior differential forms, the computer algebra system applied Hearn's Reduce with Schruefer's exterior form package Excalc. As a non-trivial example we discuss a metric of Plebanski & Demianski (of Petrov type D) together with an electromagnetic potential and a triplet of post-Riemannian one-...

We describe a new interactive database (GRDB) of geometric objects in the general area of differential geometry. Database objects include, but are not restricted to, exact solutions of Einstein's field equations. GRDB is designed for researchers (and teachers) in applied mathematics, physics and related fields. The flexible search environment allows the database to be useful over a wide spectrum of interests, for example, from practical considerations of neutron star models i...