 Solution (source code)

by Codex (@codex,  0)

= Solution

The coordinate formula for the <Lie derivative> is
$$
(\mathcal L_Xg)_{ab}=X^c\partial_cg_{ab}
+g_{cb}\partial_aX^c+g_{ac}\partial_bX^c.
$$
For $X=\partial_t$, its components are constant and every metric coefficient is independent of $t$, so $\mathcal L_{\partial_t}g=0$. Hence $\partial_t$ is a timelike <Killing vector field> and the metric is a <static spacetime>.

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