General Relativity - U02 ComputerLab Curvature with xTensor and Mathematica

Use of the xTensor Mathematica package to do symbolic computations in General Relativity xTensor is part of the xAct package. It is open source, under a GPL license and can be found at: http://www.xact.es . Symmetries of the Riemann tensor . Contractions of the Riemann tensor: Ricci, Einstein, Scalar Curvature, trace free Ricci and Weyl . Manipulating expressions using the above tensors: RiemannToChristoffel, EinsteinToRicci, WeylToRiemann, TFRicciToRicci . Commutator of covariant derivative: SortCovDs, CommuteCovDs . Rules and substitutions: MakeRule, IndexSet, IndexRule . Exercise: Bianchi identities . Exercise: proof of the geodesic deviation equation . Exercise: DD ξ = R ξ Notebooks provided at the course's website: http://www.physics.ntua.gr/konstant/GR/videos.html ------------------------------------------------------------ Supplementary material for the undergraduate course “General Relativity and Cosmology” offered at the Physics Department of the School of Applied Mathematical and Physical Sciences of the National Technical University of Athens (NTUA). Related page: http://physics.ntua.gr/konstant/GR/ Instructor: Konstantinos N. Anagnostopoulos (spring 2023), Associate Professor of Physics, NTUA http://physics.ntua.gr/konstant