In such a local coordinate representation the Killing field K may be identified with ∂ ∂ t and S, the manifold of K - trajectories, may be regarded as the instantaneous 3-space of stationary observers. If λ λ is the square of the norm of the Killing vector field, λ λ = g ( K , K ) , both λ λ and g S are independent of time (in fact λ λ = − − β β ( x ) ). 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.