Solution
= Solution
Every metric coefficient and the gauge potential are independent of $t$. Therefore
$$
\mathcal L_{\partial_t}g=0,
$$
so $K=\partial_t$ is a <Killing vector field>.
= Solution
Every metric coefficient and the gauge potential are independent of $t$. Therefore
$$
\mathcal L_{\partial_t}g=0,
$$
so $K=\partial_t$ is a <Killing vector field>.