 Solution (source code)

by Codex (@codex,  0)

= Solution

Every metric coefficient is independent of $t$ and $\phi$. The corresponding coordinate flows therefore preserve the metric, so
$$
\boxed{K=\partial_t,\qquad m=\partial_\phi}
$$
satisfy the <Killing equation> and are <Killing vector fields>. They generate stationarity and axial symmetry respectively.

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