The Riemann Curvature Tensor (Lecture скачать в хорошем качестве

The Riemann Curvature Tensor (Lecture

Part 4 Tensor Formalism for GR (Book Ch 11, and video lectures #16 to #17) Course textbook: A College Course on Relativity and Cosmology by Ta-Pei Cheng https://global.oup.com/academic/produ... Description: The more difficult topic of deriving Riemann curvature tensor is presented here. In this way, the Einstein field equation is justified with the proper mathematics. Chapter 11 may be viewed as the math appendix of the book. Viewers less interested in the mathematical aspect of GR can skip over and go directly to Parts 5 - 8 (black holes & cosmology). Learning objective: Viewers should enjoy seeing some of the basic features of differential geometry (covariant differentiation and parallel transport, etc.) for a proper formulation of general relativity. One can then derive the Riemann curvature tensor by parallel transporting a vector around a closed path, or through the equation of geodesic deviation. From the Principle of General Covariance, one can then derive the GR equation of motion as well as the Einstein field equation (with the help of Bianchi identity). With this math background, a viewer should also be able to understand the Action-Principle approach to the GR field equation.