Timeline for Clarification on tetrad indices
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 12, 2016 at 5:41 | vote | accept | GregVoit | ||
| Aug 12, 2016 at 5:40 | comment | added | Futurologist | No, I think such index "commutativity" does not hold in general. I simply mean that the notation is, as you said it yourself, taking the $k$-th component of the covariant derivative $(\nabla_{F_4}F_3)^k = (F_4^l \nabla_l F_3)^k = F_4^l (\nabla_l F_3)^k$ is written as $F_4^l \nabla_l F_3^{\, k}$. Simply the parentheses are omitted. In general $$(\nabla_l v)^k \partial_k = \nabla_l ( v^k ) \partial_k + v^j \Gamma_{ l j }^k \partial_k$$ | |
| Aug 12, 2016 at 5:04 | comment | added | GregVoit | so are you saying that in this notation, $\nabla_{l}(v^{k})=\left(\nabla_{l}v\right)^{k}$? @Futurologist | |
| Aug 12, 2016 at 4:24 | history | answered | Futurologist | CC BY-SA 3.0 |