Episode 136: Introduction to General Relativity
The Science of Everything Podcast
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The Riemann Curvature Tensor
The Riemann curvature tensor is quite a complex object. It has 256 components but thanks to symmetry and various other properties that we didn't get into here some of them relating to the fact that it's a tensor so it must be invariant to certain types of coordinate transformations. Thanks to various mathematical tricks and symmetries only 20 of these 256 components are independent of each other and non-zero. Theoretically this giant monster has 256 Components but only 20 of them are actually different from each other. That's still a lot but at least it's a bit more manageable. Now let's see how Einstein's field equations work in curved spacetime.
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