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.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 311 / 2 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-311/2/a/solution