General Theory of Relativity or the theory of relativistic gravitation is the one most famous branch of theoretical physics. Everybody heard about black holes, gravitational waves and expanding Universe. The goal of this online course is to introduce you into this theory and to give the precise meaning to these notions. The introduction is based on the consideration of many practical generic examples in various scopes of the General Relativity. Once you complete this HSE online course you will be able to solve basic standard problems of this theory. We assume that you are familiar with the Special Theory of Relativity and Classical Electrodynamics. However, as an aid to the distant study we have recorded several complementary materials which are supposed to help you understand some of the aspects of the Special Theory of Relativity and Classical Electrodynamics and some of the calculational tools that are used in our course. Also as a complementary material we provide the written form of the lectures at the website: https://math.hse.ru/generalrelativity2015 Do you have technical problems? Write to us: coursera@hse.ru
Covariant differentiation(part 2)
Reseñas
4.4 (159 calificaciones)
24 de may. de 2018
Very helpful. I recommend for those who already have some familiarity with GR, or with tensors and differential geometry.
17 de jul. de 2017
One of the most important courses ever taken and yet. still difficult to understand really well.
De la lección
Covariant differential and Riemann tensor
We start with the definition of what is tensor in a general curved space-time. Then we define what is connection, parallel transport and covariant differential. We show that for Riemannian manifolds connection coincides with the Christoffel symbols and geodesic equations acquire a clear geometric meaning. We end up with the definition of the Riemann tensor and the description of its properties. We explain how Riemann tensor allows to distinguish flat space-time in curved coordinates from curved space-times. For this module we provide complementary video to help students to recall properties of tensors in flat space-time.
Impartido por:
Emil Akhmedov
Associate Professor
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