Understanding Geodesics and Curvature Tensor using SageMath

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  • 測地線・曲率テンソルとSageMath
  • ソクチセン ・ キョクリツ テンソル ト SageMath

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The curvature tensor of 4-dimensional spacetime, which appears in general relativity, is difficult to understand because it is a complex tensor with four subscripts. Since it is impossible to visualize geodesics and curvatures in 4-dimensional spacetime, we visualized geodesics and calculate curvature tensors of 2-dimensional surfaces, which corresponds to a 2-dimensional Riemann plane in 3-dimensional Euclidean space in order to understand the meanings of geodesics and curvature tensors. For the visualization and the calculation, we used SageMath, which is a free computer algebra system software. We found that the visualization of these geodesics and the calculation of curvatures on a 2-dimensional surface in 3-dimensional Euclidean space is useful for understanding their meanings. The usefulness of SageMath is also clarified.

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