- #1
member 428835
Hi PF!
I'm trying to compute
$$
\frac{1}{\sqrt g}\frac{\partial}{\partial u^\mu}\left( \sqrt g g^{\mu v} \frac{\partial \eta(s,\phi))}{\partial u^v} \right)
$$
where I found
$$
\sqrt g = \csc^2\alpha \sin s\\
g =
\begin{bmatrix}
\csc^2\alpha &0\\
0 & \csc^2\alpha\sin^2 s
\end{bmatrix}
$$
where ##\mu,v = 1,2##. Can someone help me out here? I can link the paper I'm reading this from if it helps, but I think I've communicated everything relevant.
I'm trying to compute
$$
\frac{1}{\sqrt g}\frac{\partial}{\partial u^\mu}\left( \sqrt g g^{\mu v} \frac{\partial \eta(s,\phi))}{\partial u^v} \right)
$$
where I found
$$
\sqrt g = \csc^2\alpha \sin s\\
g =
\begin{bmatrix}
\csc^2\alpha &0\\
0 & \csc^2\alpha\sin^2 s
\end{bmatrix}
$$
where ##\mu,v = 1,2##. Can someone help me out here? I can link the paper I'm reading this from if it helps, but I think I've communicated everything relevant.
