18. Killing's Equation In Section 8.2, a Killing vector corresponding to symmetry of the metric was defined in a coordinate system in which the metric was independent of one coordinate, x. The components of the corresponding Killing vector are then (0, 1, 0, 0). By explicit calculation, show that This is Killing's equation. It is a general characterization of Killing vectors in the sense that any solution corresponds to a symmetry of the metric.