Anchovyforestbane Posted November 17, 2020 Share Posted November 17, 2020 It appears I cannot find anything that adequately explains Christoffel Notation and what it means. All I know is that it is used to describe the affine geometry of spacetime, and by extent in calculating spacetime geodesics; but I've yet to understand how, or how to use it. Link to comment Share on other sites More sharing options...
mathematic Posted November 18, 2020 Share Posted November 18, 2020 The notation is math, mot physics. https://en.wikipedia.org/wiki/Christoffel_symbols Link to comment Share on other sites More sharing options...
joigus Posted November 18, 2020 Share Posted November 18, 2020 There are many good books that explain Christoffel symbols. It's not a notation; it's a real object that you need to correct for the fact that your reference directions change depending on the point when you're taking derivatives of vectors. A very good classic book is Lovelock & Rund: https://www.amazon.com/Tensors-Differential-Variational-Principles-Mathematics/dp/0486658406 Link to comment Share on other sites More sharing options...
Markus Hanke Posted November 18, 2020 Share Posted November 18, 2020 15 hours ago, Anchovyforestbane said: It appears I cannot find anything that adequately explains Christoffel Notation and what it means. All I know is that it is used to describe the affine geometry of spacetime, and by extent in calculating spacetime geodesics; but I've yet to understand how, or how to use it. Have a look here: https://einsteinrelativelyeasy.com/index.php/dictionary/25-christoffel-symbol Essentially, the Christoffel symbols (of the 2nd kind) tell you how the components of your basis vectors in a given coordinate system change as you move around a manifold. If you want to define a concept of a covariant derivative - which by definition needs to be consistent everywhere on the manifold -, you need to compensate for this change, which is why the Christoffel symbols appear in the definition of the covariant derivative. 1 Link to comment Share on other sites More sharing options...
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