Coordinate time ($t=x^0$)

Coordinate time labels events in a chosen spacetime chart. It is distinct from proper time, which is measured by a clock along its timelike path. For a stationary observer in a static metric with signature $(+---)$, the rate is $d\tau =\sqrt{g_{tt}}dt$ in units with light speed one. Different stationary observers can therefore accumulate different proper times during the same coordinate-time interval.