The use of the algebraic programming in teaching general relativity

Einstein's general relativity is the best available theory of gravity. In recent years, spectacular proofs of Einstein's theory have been conducted, which have aroused interest that goes far beyond the narrow circle of specialists. The aim of this work is to offer an elementary introduction to general relativity. In this first part, we introduce the geometric concepts that constitute the basis of Einstein's theory. In the second part we will use these concepts to explore the ...

These lectures notes contain an introduction to General Relativity. They are addressed to a general mathematical audience with no specific background in physics. The goal is to motivate and explain Einstein's theory of gravity and discuss some of the fundamental examples.

In the present paper, we describe some experiences in using programming, commands and graphical interfaces based on computer algebra systems, as tools for learning Physics and Mathematics.

This text aims to explain general relativity to geometers who have no knowledge about physics. Using handwritten notes by Michel Vaugon, we construct the bases of the theory.

This is a brief introduction to general relativity, designed for both students and teachers of the subject. While there are many excellent expositions of general relativity, few adequately explain the geometrical meaning of the basic equation of the theory: Einstein's equation. Here we give a simple formulation of this equation in terms of the motion of freely falling test particles. We also sketch some of its consequences, and explain how the formulation given here is equiva...

We present a small computer algebra program for use in Maxwell's theory. The Maxwell equations and the energy-momentum current of the electromagnetic field are formulated in the language of exterior differential forms. The corresponding program can be applied (in the presence of a gravitational field) in curved Riemannian spacetime as well as in flat Minkowski spacetime in inertial or {\em non-inertial} frames. Our program is written for the computer algebra system REDUCE wit...

This paper gives a self-contained, elementary, and largely pictorial statement of Einstein's equation.

We report on selected oral contributions to the A2 session "Mathematical relativity and other progress in classical gravity theory" of "The 20th International Conference on General Relativity and Gravitation (GR20)" in Warsaw.

In this paper we describe an algorithm to determine the vectors normal to a space-time V4 embedded in a pseudo-Euclidean manifold M4+n. An application of this algorithm is given considering the Schwarzchild space-time geometry embedded in a 6 dimensional pseudo-Euclidean manifold, using the algebraic computing system REDUCE.

DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in grav...