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In general relativity, a spacetime is said to be static if it admits a global, non-vanishing, timelike Killing vector field which is irrotational, ''i.e.'', whose orthogonal distribution is involutive. (Note that the leaves of the associated foliation are necessarily space-like hypersurfaces.) Thus, a static spacetime is a stationary spacetime satisfying this additional integrability condition. These spacetimes form one of the simplest classes of Lorentzian manifolds. Locally, every static spacetime looks like a standard static spacetime which is a Lorentzian warped product ''R'' ''S'' with a metric of the form , where ''R'' is the real line, is a (positive definite) metric and is a positive function on the Riemannian manifold ''S''. In such a local coordinate representation the Killing field may be identified with and ''S'', the manifold of -''trajectories'', may be regarded as the instantaneous 3-space of stationary observers. If is the square of the norm of the Killing vector field, , both and are independent of time (in fact ). 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. ==Examples of static spacetimes== #The (exterior) Schwarzschild solution #de Sitter space (the portion of it covered by the static patch). #Reissner-Nordström space #The Weyl solution, a static axisymmetric solution of the Einstein vacuum field equations discovered by Hermann Weyl 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「static spacetime」の詳細全文を読む スポンサード リンク
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