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Rainich-Type Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre

Research Vignettes

In this second of two worksheets I continue describing local Rainich-type conditions which are necessary and sufficient for the metric to define a null electrovacuum. In other words, these conditions, which I will call the null electrovacuum conditions, guarantee the existence of a null electromagnetic field such that the metric and electromagnetic field satisfy the Einstein-Maxwell equations. When it exists, the electromagnetic field is easily constructed from the metric. In this worksheet I consider the null electrovacuum conditions which apply when a certain null geodesic congruence determined by the metric is twisting. I shall illustrate the these conditions using a …

Gr 20 Workshop, Warsaw, July 2013, Ian M. Anderson, Charles G. Torre

Presentations

These are the Maple worksheets used at the Differential Geometry in Maple Workshop, which was held at the 20th International Conference on General Relativity and Gravitation, in Warsaw, July 2013.

There are 6 worksheets which can be downloaded from the list of files below.

How To Find Killing Vectors, Charles G. Torre

How to... in 10 minutes or less

We show how to compute the Lie algebra of Killing vector fields of a metric in Maple using the commands KillingVectors and LieAlgebraData. A Maple worksheet and a PDF version can be found below.

How To Find A Levi Decomposition Of A Lie Algebra, Ian M. Anderson

How to... in 10 minutes or less

We show how to compute the Levi decomposition of a Lie algebra in Maple using the command LeviDecomposition. A worksheet and corresponding PDF can be found below.

How To Create A Jordan Algebra, Ian M. Anderson, Thomas J. Apedaile

How to... in 10 minutes or less

We show how to create a Jordan algebra in Maple using the commands AlgebraLibraryData and AlgebraData.

How To Create The Quaternion & Octonion Algebras, Ian M. Anderson, Thomas J. Apedaile

How to... in 10 minutes or less

We show how to create the quaternion and octonion algebras with the DifferentialGeometry software. For each algebra, there is a split-form also available.