General Relativity - U02 ComputerLab Mathematica xTensor Introduction

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 . Downloading and installing . Documentation, and online help . Defining a Manifold and its vector bundle . Defining tensors . Abstract index notation: contractions, tensor products . Metric, Levi-Civita tensor, Kronecker's deltas . Covariant derivative (Christoffel connection of metric+partial derivative) . Christoffel symbols . Lie derivatives and Lie brackets. . Exercise: prove that L_[u,v] = [L_u,L_v], when acting on vectors 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