Timeline for Covariant Derivative of New Timelike coordinate
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 1, 2022 at 22:17 | comment | added | user345249 | Yes, that answers my question. Thank you. | |
| Sep 1, 2022 at 21:09 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
edited tags
|
| Sep 1, 2022 at 20:50 | comment | added | peek-a-boo | $\nabla^af=g^{ab}\nabla_bf=g^{ab}(df)_b=g^{ab}\frac{\partial f}{\partial x^b}$ if that’s what you want to know. This is what we’d call the ($a^{th}$ component of) gradient vector field of $f$, i.e $\text{grad}_g(f)$. | |
| Sep 1, 2022 at 20:47 | comment | added | user345249 | Would the covariant derivative with raised indice also just be the regular derivative in this case? | |
| Sep 1, 2022 at 19:57 | comment | added | peek-a-boo | $\tau$ is a coordinate, meaning it is a function. It’s covariant derivative is by definition simply its exterior derivative/differential $d\tau$. CHecking whether this is timeline/space like amounts to looking at the sign of the coefficient of $d\tau^2$ in the metric. | |
| Sep 1, 2022 at 19:48 | history | asked | user345249 | CC BY-SA 4.0 |