Symbolic and Numerical Analysis in General Relativity with Open Source Computer Algebra Systems
arXiv:1703.09738 · doi:10.1007/s10714-018-2486-x
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
References in corpus (5)
- Confluent Heun functions and the physics of black holes: resonant frequencies, Hawking radiation and scattering of scalar waves
- Examples of Heun and Mathieu functions as solutions of wave equations in curved spaces
- Quantum Field Theory Applications of Heun Type Functions
- Tensor manipulation in GPL Maxima
- Symbolic tensor calculus on manifolds: a SageMath implementation