Symbolic and numerical analysis in general relativity with open source computer algebra systems
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.
- Publication:
-
General Relativity and Gravitation
- Pub Date:
- January 2019
- DOI:
- 10.1007/s10714-018-2486-x
- arXiv:
- arXiv:1703.09738
- Bibcode:
- 2019GReGr..51....4B
- Keywords:
-
- Symbolic analysis;
- Numerical analysis;
- Wave equations;
- Geodesic motion;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory;
- Physics - Computational Physics
- E-Print:
- 21 pages, 4 figures. Updated to match the published version