What are the sufficient / necessary conditions for a metric to be stationary / static? - If the metric components are independent of time in some coordinate system , is this sufficient for stationary? - I've read for static if a time-like killing vector is orthogonal to a family of hyper-surfaces than it's static and that this condition is equivalent to there being no cross terms containing ##dt##. How are these 2 conditions equivalent? I have no idea how to go about showing this? Many thanks in advance.