Date of Award
Maple is a mathematical software program containing packages of tools that may be used in making difficult computations. The Tensor sub-package of Maple's Differential Geometry package is a collection of commands used for making tensor computations on manifolds. We present a series of new tools for the Tensor package. Included with these tools are new commands to compute objects of geometric and physical interest -energy-momentum tensors, matter field equations, the Bel-Robinson tensor, etc. -along with tools to compute the geometric properties of these objects. Additionally, an electronic database of exact solutions to the Einstein field equations has been created for use within the Differential Geometry package. Several geometric and algebraic properties of each Lorentz metric, including Killing vector fields, orbits and isometry groups, orthonormal frames, and Petrov types, have been computed and are included in this database. To provide researchers with a mechanism for utilizing elements of this exact solutions database, a graphical user interface has also been developed. Applications of the new tools in the Tensor package are extensive, and will provide researchers with a more useful interface for investigating problems in theoretical physics and mathematics.
Chamberlin, Sydney JoAnne, "Algebraic computing Tools in General Relativity: Energy-Momentum Tensors and Exact Solutions to the Einstein Field Equations" (2009). Undergraduate Honors Capstone Projects. 14.
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