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Graph, Wall, Tome: Difference between revisions
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[https://www.youtube.com/watch?v=UfThVvBWZxM&t=12m6s Explanation of $$R$$] | [https://www.youtube.com/watch?v=UfThVvBWZxM&t=12m6s Explanation of $$R$$] | ||
$$R$$ is the curvature of the spacetime manifold at each point along the manifold. It's based on a concept of 'parallel transport', where you move a vector around some path on the manifold. $$R$$ can be computed at each point on the manifold, and describes the difference in the vector's angle after following an infinitesimally small path around the neighborhood of that point. The video does a great job of visualizing when and why that vector angle change would happen, with flat vs. curved manifolds. | $$R$$ is a scalar value, describing the "curvature of the spacetime manifold" at each point along the manifold. It's based on a concept of 'parallel transport', where you move a vector around some path on the manifold. | ||
$$R$$ can be computed at each point on the manifold, and describes the difference in the vector's angle after following an infinitesimally small path around the neighborhood of that point, vs. what it was originally. The video does a great job of visualizing when and why that vector angle change would happen, with flat vs. curved manifolds. | |||
In the video, they focus first on the curvature of space. Hopefully they incorporate back in curvature in time, because that's less obvious. | In the video, they focus first on the curvature of space. Hopefully they incorporate back in curvature in time, because that's less obvious. | ||
==== $$R_{\mu v}$$ ==== | ==== $$R_{\mu v}$$ ==== | ||