In general relativity, a spacetime is said to be static if it does not change over time and is also irrotational.
Thus, the Kerr solution provides an example of a stationary spacetime that is not static; the non-rotating Schwarzschild solution is an example that is static.
Formally, a spacetime is static if it admits a global, non-vanishing, timelike Killing vector field
(Note that the leaves of the associated foliation are necessarily space-like hypersurfaces.)
These spacetimes form one of the simplest classes of Lorentzian manifolds.
is a positive function on the Riemannian manifold S. In such a local coordinate representation the Killing field
is the square of the norm of the Killing vector field,
It is from the latter fact that a static spacetime obtains its name, as the geometry of the space-like slice S does not change over time.
Some explicit examples include: This relativity-related article is a stub.