Publication: Symbolic and numerical analysis in general relativity with open source computer algebra systems
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Publisher
Springer Science and Business Media LLC
Type
Abstract
We study three computer algebra systems, namely SageMath (with SageManifolds package), Maxima (with ctensor package) and Python language (with GraviPy module), which allow tensor manipulation for general relativity calculations along with general algebraic calculations. We present a benchmark of these systems using simple examples. After the general analysis, we focus on the SageMath and SageManifolds system to derive, analyze and visualize the solutions of the massless Klein-Gordon equation and geodesic motion with Hamilton-Jacobi formalism. We compare our numerical result of the Klein-Gordon equation with the asymptotic form of the analytical solution to see that they agree.
21 pages, 4 figures. Updated to match the published version
21 pages, 4 figures. Updated to match the published version
Description
Journal or Series
General Relativity and Gravitation
ISSN
0001-7701
ISBN
Rights
OPEN
Keywords
High Energy Physics - Theory, Hamilton-Jacobi formalism, numerical analysis, FOS: Physical sciences, Equations of motion in general relativity and gravitational theory, General Relativity and Quantum Cosmology (gr-qc), Computational Physics (physics.comp-ph), Hamilton-Jacobi equations in mechanics, General Relativity and Quantum Cosmology, High Energy Physics - Theory (hep-th), symbolic analysis, geodesic motion, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Wave equation, Computational methods for problems pertaining to relativity and gravitational theory, Klein-Gordon equation, wave equations, Physics - Computational Physics