A stationary spacetime admits a Killing vector field that is timelike in the region representing stationary observers, in particular near infinity for an asymptotically flat stationary black hole.
A static spacetime has a timelike Killing vector that is hypersurface orthogonal. Coordinates adapted to it can be chosen with no time-space cross terms.
A stationary axisymmetric spacetime has commuting stationary and axial Killing vector fields, with the axial field having closed spacelike orbits.
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In the context of general relativity and the study of spacetimes, "stationary spacetime" refers to a specific type of spacetime that possesses certain symmetries, particularly time invariance. A stationary spacetime is characterized by the following features: 1. **Time Independence**: The geometry of the spacetime does not change with time.