Symbolic and numerical analysis in general relativity with open source computer algebra systems


Birkandan T. , GÜZELGÜN C., ŞIRIN E., USLU M. C.

GENERAL RELATIVITY AND GRAVITATION, cilt.51, sa.1, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 51 Konu: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s10714-018-2486-x
  • Dergi Adı: GENERAL RELATIVITY AND GRAVITATION

Özet

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.