\begin{dmath}
g_{0{}0}=\frac{-1}{u^2}
\end{dmath}
\begin{dmath}
g_{1{}1}=a^2 u^2
\end{dmath}
\begin{dmath}
g_{2{}2}=\sin\left(x^{1}\right)^2 a^2 u^2
\end{dmath}
\begin{dmath}
g_{3{}3}=u^2
\end{dmath}
