- #1
sunrah
- 199
- 22
I've just done a derivation and had to use the following
[itex]u_{b}u^{c}\partial_{c}\rho = u_{b}\frac{dx^{c}}{d\tau}\frac{\partial\rho}{\partial x^{c}} = u_{b}\frac{d\rho}{d\tau}[/itex]
We've done this cancellation a lot during my GR course, but I'm not clear exactly when/why this is possible.
EDIT: is this only true in inertial coordinates?
[itex]u_{b}u^{c}\partial_{c}\rho = u_{b}\frac{dx^{c}}{d\tau}\frac{\partial\rho}{\partial x^{c}} = u_{b}\frac{d\rho}{d\tau}[/itex]
We've done this cancellation a lot during my GR course, but I'm not clear exactly when/why this is possible.
EDIT: is this only true in inertial coordinates?