Timeline for How is the scalar product between two vectors defined in general relativity?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 2, 2021 at 21:37 | comment | added | HelloGoodbye | "The action of the metric on two vectors is so useful that it gets its own name, the inner product (or scalar product, or dot product): $\eta(V,W)=\eta_{\mu\nu}V^\mu W^\nu=V\cdot W.$" | |
| Oct 2, 2021 at 21:34 | vote | accept | HelloGoodbye | ||
| Oct 2, 2021 at 21:32 | comment | added | HelloGoodbye | It is used for example in Carroll's Spacetime and Geometry: An Introduction to General Relativity. It's the same as the notation for the dot product used in linear algebra. | |
| Oct 2, 2021 at 21:06 | comment | added | user1379857 | I have not really seen that notation but I can't imagine what else $u \cdot v$ could be. There aren't many options. | |
| Oct 2, 2021 at 13:21 | comment | added | HelloGoodbye | Thanks, that makes sense. I often see the notation $u\cdot v$. Is this defined as $g(u,v)$, in contrast to simply being the product of $u$ and $v$, i.e., $uv$? | |
| Oct 2, 2021 at 5:57 | history | answered | user1379857 | CC BY-SA 4.0 |