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691:). It is from the latter fact that a static spacetime obtains its name, as the geometry of the space-like slice
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199:, which is the geometry of a stationary spacetime that does not change in time but can rotate. Thus, the
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satisfying this additional integrability condition. These spacetimes form one of the simplest classes of
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In general, "almost all" spacetimes will not be static. Some explicit examples include:
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if it does not change over time and is also irrotational. It is a special case of a
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Formally, a spacetime is static if it admits a global, non-vanishing,
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Spacetime which does not change over time and is irrotational
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is the square of the norm of the
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provides an example of a stationary spacetime that is
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256:. (Note that the leaves of the associated
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171:Learn how and when to remove this message
109:Learn how and when to remove this message
812:Hawking, S. W.; Ellis, G. F. R. (1973),
395:{\displaystyle g=-\beta (x)dt^{2}+g_{S}}
134:This article includes a list of general
814:The large scale structure of space-time
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279:which is a Lorentzian warped product
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437:is a (positive definite) metric and
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47:adding citations to reliable sources
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684:{\displaystyle \lambda =-\beta (x)}
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714:(the portion of it covered by the
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140:it lacks sufficient corresponding
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776:Examples of non-static spacetimes
653:are independent of time (in fact
264:.) Thus, a static spacetime is a
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801:in them are not even stationary.
785:Spherically symmetric spacetimes
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599:{\displaystyle \lambda =g(K,K)}
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760:{\displaystyle R_{\mu \nu }=0}
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695:does not change over time.
260:are necessarily space-like
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305:with a metric of the form
277:standard static spacetime
207:static; the non-rotating
619:{\displaystyle \lambda }
558:{\displaystyle \lambda }
490:may be identified with
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250:orthogonal distribution
155:more precise citations.
844:-related article is a
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32:This article
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850:expanding it
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769:Hermann Weyl
716:static patch
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543:trajectories
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41:Please help
36:verification
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153:introducing
889:Categories
842:relativity
806:References
254:involutive
161:April 2021
136:references
99:April 2021
69:newspapers
747:ν
744:μ
670:β
667:−
661:λ
614:λ
573:λ
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499:∂
445:β
346:β
343:−
290:×
258:foliation
240:which is
189:spacetime
248:, whose
216:timelike
822:0424186
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149:improve
83:scholar
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724:space.
406:where
193:static
138:, but
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90:JSTOR
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846:stub
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626:and
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187:, a
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