Graph, Wall, Tome: Difference between revisions
→What are $$R_{\mu v}$$ and $$R$$ geometrically?
| Line 120: | Line 120: | ||
Einstein’s original publication, Die Feldgleichungen der Gravitation, in English | Einstein’s original publication, Die Feldgleichungen der Gravitation, in English | ||
==== R ==== | ==== $$R$$ ==== | ||
[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. In the video, they focus first on the curvature of space. Hopefully they incorporate back in curvature in time, because that's less obvious. | $$R$$ 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. | ||
In the video, they focus first on the curvature of space. Hopefully they incorporate back in curvature in time, because that's less obvious. | |||
==== $$R_{\mu v}$$ ==== | |||
The same video then proceeds to explain $$R_{\mu v}$$. It progresses through some concepts. | |||
=== How do they relate? === | === How do they relate? === | ||