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Turing jump - Revision history
2024-03-29T07:10:02Z
Revision history for this page on the wiki
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en>Rjwilmsi: /* References */Added 1 doi to a journal cite using AWB (10388)
2014-08-19T13:02:40Z
<p><span dir="auto"><span class="autocomment">References: </span>Added 1 doi to a journal cite using <a href="/index.php?title=Testwiki:AWB&action=edit&redlink=1" class="new" title="Testwiki:AWB (page does not exist)">AWB</a> (10388)</span></p>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">{{Expert-subject|Physics|date=November 2008}}</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">I</ins>'<ins style="font-weight: bold; text-decoration: none;">m Thad </ins>and <ins style="font-weight: bold; text-decoration: none;">I live </ins>with <ins style="font-weight: bold; text-decoration: none;">my husband </ins>and <ins style="font-weight: bold; text-decoration: none;">our two children in Dirksland</ins>, <ins style="font-weight: bold; text-decoration: none;">in </ins>the <ins style="font-weight: bold; text-decoration: none;">ZH south area</ins>. <ins style="font-weight: bold; text-decoration: none;">My hobbies are Homebrewing</ins>, <ins style="font-weight: bold; text-decoration: none;">Bonsai </ins>and <ins style="font-weight: bold; text-decoration: none;">Auto audiophilia.</ins><<ins style="font-weight: bold; text-decoration: none;">br</ins>><<ins style="font-weight: bold; text-decoration: none;">br</ins>><ins style="font-weight: bold; text-decoration: none;">Feel free to visit my web blog .</ins>.. <ins style="font-weight: bold; text-decoration: none;">fifa 15 coin generator </ins>([http://<ins style="font-weight: bold; text-decoration: none;">Asadimpex</ins>.<ins style="font-weight: bold; text-decoration: none;">com</ins>/<ins style="font-weight: bold; text-decoration: none;">?p=1 </ins>http://<ins style="font-weight: bold; text-decoration: none;">asadimpex</ins>.<ins style="font-weight: bold; text-decoration: none;">com</ins>/<ins style="font-weight: bold; text-decoration: none;">?p=1</ins>]<ins style="font-weight: bold; text-decoration: none;">)</ins></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">In [[general relativity]], a [[spacetime]] is said to be '''static''' if it admits a global, non-vanishing, [[timelike]] [[Killing vector field]] <math>K</math> which is '''irrotational''', ''i.e.</del>'<del style="font-weight: bold; text-decoration: none;">', whose [[orthogonal distribution]] is [[involutive]]. (Note that the leaves of the associated [[foliation]] are necessarily space-like [[hypersurface]]s.) Thus, a static spacetime is a [[stationary spacetime]] satisfying this additional integrability condition. These spacetimes form one of the simplest classes of [[Lorentzian manifold]]s. </del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Locally, every static spacetime looks like a '''standard static spacetime''' which is a Lorentzian warped product ''R'' <math>\times</math> ''S'' with a metric of the form</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><math>g[(t,x)] = -\beta(x) dt^{2} + g_{S}[x]</math>,</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">where ''R'' is the real line, <math>g_{S}</math> is a (positive definite) metric </del>and <del style="font-weight: bold; text-decoration: none;"><math>\beta</math> is a positive function on the [[Riemannian manifold]] ''S''.</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">In such a local coordinate representation the [[Killing vector field|Killing field]] <math>K</math> may be identified </del>with <del style="font-weight: bold; text-decoration: none;"><math>\partial_t</math> </del>and <del style="font-weight: bold; text-decoration: none;">''S''</del>, the <del style="font-weight: bold; text-decoration: none;">manifold of <math>K</math>-''trajectories'', may be regarded as the instantaneous 3-space of stationary observers</del>. <del style="font-weight: bold; text-decoration: none;">If <math>\lambda</math> is the square of the norm of the Killing vector field, <math>\lambda = g(K,K)</math></del>, <del style="font-weight: bold; text-decoration: none;">both <math>\lambda</math> </del>and <<del style="font-weight: bold; text-decoration: none;">math</del>><del style="font-weight: bold; text-decoration: none;">g_S</del><<del style="font-weight: bold; text-decoration: none;">/math</del>> <del style="font-weight: bold; text-decoration: none;">are independent of time (in fact <math>\lambda = - \beta(x)</math>)</del>. <del style="font-weight: bold; text-decoration: none;">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</del>.</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">==Examples of static spacetimes==</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">#The </del>(<del style="font-weight: bold; text-decoration: none;">exterior) [[Schwarzschild solution]]</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">#[[de Sitter space]] (the portion of it covered by the [[De Sitter space#Static coordinates|static patch]]).</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">#[[Reissner-Nordström]] space</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">#The [[Weyl solution]], a static axisymmetric solution of the Einstein vacuum field equations <math>R_{\mu\nu} = 0</math> discovered by [[Hermann Weyl]]</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">==External links==</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">* </del>[http://<del style="font-weight: bold; text-decoration: none;">www.rqgravity</del>.<del style="font-weight: bold; text-decoration: none;">net</del>/<del style="font-weight: bold; text-decoration: none;">GeneralRelativity#StationaryObservers Concepts of General Relativity ] - A first principles demonstration of the metric in static spacetime</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">* [</del>http://<del style="font-weight: bold; text-decoration: none;">arxiv</del>.<del style="font-weight: bold; text-decoration: none;">org</del>/<del style="font-weight: bold; text-decoration: none;">abs/math/0406332v2 M. Sanchez, On the geometry of static space-times, preprint, 2004.]</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">{{relativity-stub}}</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">[[Category:Lorentzian manifolds]</del>]</div></td><td colspan="2" class="diff-side-added"></td></tr>
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en>Rjwilmsi
https://en.formulasearchengine.com/index.php?title=Turing_jump&diff=9093&oldid=prev
en>Monkbot: /* References */Fix CS1 deprecated date parameter errors
2014-01-31T03:32:02Z
<p><span dir="auto"><span class="autocomment">References: </span>Fix <a href="/index.php?title=Help:CS1_errors&action=edit&redlink=1" class="new" title="Help:CS1 errors (page does not exist)">CS1 deprecated date parameter errors</a></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 04:32, 31 January 2014</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Epoxy resins are created by transforming liquid polyethers into infusible solids through </del>a <del style="font-weight: bold; text-decoration: none;">special curing process. Should you beloved this short article as well as you want to receive more info with regards </del>to [<del style="font-weight: bold; text-decoration: none;">http:</del>/<del style="font-weight: bold; text-decoration: none;">/prestont4</del>.<del style="font-weight: bold; text-decoration: none;">newsvine</del>.<del style="font-weight: bold; text-decoration: none;">com/_news/2014/06/04/24153572-respecto-a-la-versatilidad-de-la-resina-epoxi resinas epoxi</del>] <del style="font-weight: bold; text-decoration: none;">generously go to our own internet site</del>. <del style="font-weight: bold; text-decoration: none;">In most cases, resins are </del>the <del style="font-weight: bold; text-decoration: none;">result </del>of <del style="font-weight: bold; text-decoration: none;">a chemical reaction between epichlorohydrin and bisphenol</del>-<del style="font-weight: bold; text-decoration: none;">A</del>. <del style="font-weight: bold; text-decoration: none;">Overall</del>, the <del style="font-weight: bold; text-decoration: none;">creation </del>of <del style="font-weight: bold; text-decoration: none;">epoxy resin </del>is <del style="font-weight: bold; text-decoration: none;">part </del>of <del style="font-weight: bold; text-decoration: none;">an industry that generates over $15 billion US Dollars annually.</del><<del style="font-weight: bold; text-decoration: none;">br</del>><<del style="font-weight: bold; text-decoration: none;">br</del>><del style="font-weight: bold; text-decoration: none;">Epoxy resins have many different uses. For example</del>, <del style="font-weight: bold; text-decoration: none;">resins that are cured through exposure to ultraviolet light are commonly used in fiber optics, optoelectronics</del>, and <del style="font-weight: bold; text-decoration: none;">dentistry. Industrial tooling applications use epoxy resins to make laminates, castings, fixtures, and molds</del>. In the <del style="font-weight: bold; text-decoration: none;">electronics industry, epoxy resins can </del>be <del style="font-weight: bold; text-decoration: none;">used to make insulators</del>, <del style="font-weight: bold; text-decoration: none;">transformers</del>, <del style="font-weight: bold; text-decoration: none;">generators, and switchgear</del>.<<del style="font-weight: bold; text-decoration: none;">br</del>><<del style="font-weight: bold; text-decoration: none;">br</del>><del style="font-weight: bold; text-decoration: none;">Around your home</del>, <del style="font-weight: bold; text-decoration: none;">epoxy resin can be valuable for repairing china</del>, <del style="font-weight: bold; text-decoration: none;">pottery, glass, wood, metal</del>, and <del style="font-weight: bold; text-decoration: none;">leather objects</del>. It <del style="font-weight: bold; text-decoration: none;">has </del>a <del style="font-weight: bold; text-decoration: none;">very strong and highly durable bond after it has set properly. Epoxy resins can be used </del>as <del style="font-weight: bold; text-decoration: none;">repair material for marine applications, but they should </del>not <del style="font-weight: bold; text-decoration: none;">be applied on </del>the <del style="font-weight: bold; text-decoration: none;">outer layer </del>of a <del style="font-weight: bold; text-decoration: none;">boat because UV light exposure will eventually cause </del>the <del style="font-weight: bold; text-decoration: none;">resin to deteriorate.</del><<del style="font-weight: bold; text-decoration: none;">br</del>><<del style="font-weight: bold; text-decoration: none;">br</del>><del style="font-weight: bold; text-decoration: none;">Additionally, epoxy resin is valuable as a crafting supply</del>. <del style="font-weight: bold; text-decoration: none;">People who enjoy making miniatures sometimes use epoxy resin to simulate water when creating beach and ocean scenes, although smaller amounts </del>of <del style="font-weight: bold; text-decoration: none;">resin can be used to design replicas </del>of <del style="font-weight: bold; text-decoration: none;">soups, liquid drinks, and fishbowls to be used </del>in <del style="font-weight: bold; text-decoration: none;">a child's dollhouse</del>. <del style="font-weight: bold; text-decoration: none;">Jewelry makers use epoxy resin to create necklaces</del>, <del style="font-weight: bold; text-decoration: none;">pins</del>, <del style="font-weight: bold; text-decoration: none;">bangles</del>, <del style="font-weight: bold; text-decoration: none;">bracelets, earrings, and rings that feature embedded glitter for a fun effect</del>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{{Expert-subject|Physics|date=November 2008}}</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In [[general relativity]], </ins>a <ins style="font-weight: bold; text-decoration: none;">[[spacetime]] is said </ins>to <ins style="font-weight: bold; text-decoration: none;">be '''static''' if it admits a global, non-vanishing, [[timelike]] [</ins>[<ins style="font-weight: bold; text-decoration: none;">Killing vector field]] <math>K<</ins>/<ins style="font-weight: bold; text-decoration: none;">math> which is '''irrotational''', ''i</ins>.<ins style="font-weight: bold; text-decoration: none;">e</ins>.<ins style="font-weight: bold; text-decoration: none;">'', whose [[orthogonal distribution]] is [[involutive]</ins>]. <ins style="font-weight: bold; text-decoration: none;">(Note that </ins>the <ins style="font-weight: bold; text-decoration: none;">leaves </ins>of <ins style="font-weight: bold; text-decoration: none;">the associated [[foliation]] are necessarily space</ins>-<ins style="font-weight: bold; text-decoration: none;">like [[hypersurface]]s</ins>.<ins style="font-weight: bold; text-decoration: none;">) Thus</ins>, <ins style="font-weight: bold; text-decoration: none;">a static spacetime is a [[stationary spacetime]] satisfying this additional integrability condition. These spacetimes form one of </ins>the <ins style="font-weight: bold; text-decoration: none;">simplest classes </ins>of <ins style="font-weight: bold; text-decoration: none;">[[Lorentzian manifold]]s. </ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Locally, every static spacetime looks like a '''standard static spacetime''' which </ins>is <ins style="font-weight: bold; text-decoration: none;">a Lorentzian warped product ''R'' <math>\times</math> ''S'' with a metric </ins>of <ins style="font-weight: bold; text-decoration: none;">the form</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><<ins style="font-weight: bold; text-decoration: none;">math</ins>><ins style="font-weight: bold; text-decoration: none;">g[(t,x)] = -\beta(x) dt^{2} + g_{S}[x]</ins><<ins style="font-weight: bold; text-decoration: none;">/math</ins>>,</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">where ''R'' is the real line</ins>, <ins style="font-weight: bold; text-decoration: none;"><math>g_{S}</math> is a (positive definite) metric </ins>and <ins style="font-weight: bold; text-decoration: none;"><math>\beta</math> is a positive function on the [[Riemannian manifold]] ''S''</ins>.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In <ins style="font-weight: bold; text-decoration: none;">such a local coordinate representation </ins>the <ins style="font-weight: bold; text-decoration: none;">[[Killing vector field|Killing field]] <math>K</math> may </ins>be <ins style="font-weight: bold; text-decoration: none;">identified with <math>\partial_t</math> and ''S''</ins>, <ins style="font-weight: bold; text-decoration: none;">the manifold of <math>K</math>-''trajectories''</ins>, <ins style="font-weight: bold; text-decoration: none;">may be regarded as the instantaneous 3-space of stationary observers</ins>. <ins style="font-weight: bold; text-decoration: none;">If </ins><<ins style="font-weight: bold; text-decoration: none;">math</ins>><ins style="font-weight: bold; text-decoration: none;">\lambda</ins><<ins style="font-weight: bold; text-decoration: none;">/math</ins>> <ins style="font-weight: bold; text-decoration: none;">is the square of the norm of the Killing vector field</ins>, <ins style="font-weight: bold; text-decoration: none;"><math>\lambda = g(K</ins>,<ins style="font-weight: bold; text-decoration: none;">K)</math></ins>, <ins style="font-weight: bold; text-decoration: none;">both <math>\lambda</math> </ins>and <ins style="font-weight: bold; text-decoration: none;"><math>g_S</math> are independent of time (in fact <math>\lambda = - \beta(x)</math>)</ins>. It <ins style="font-weight: bold; text-decoration: none;">is from the latter fact that </ins>a <ins style="font-weight: bold; text-decoration: none;">static spacetime obtains its name, </ins>as <ins style="font-weight: bold; text-decoration: none;">the geometry of the space-like slice ''S'' does </ins>not <ins style="font-weight: bold; text-decoration: none;">change over time.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Examples of static spacetimes==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">#The (exterior) [[Schwarzschild solution]]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">#[[de Sitter space]] (</ins>the <ins style="font-weight: bold; text-decoration: none;">portion </ins>of <ins style="font-weight: bold; text-decoration: none;">it covered by the [[De Sitter space#Static coordinates|static patch]]).</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">#[[Reissner-Nordström]] space</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">#The [[Weyl solution]], </ins>a <ins style="font-weight: bold; text-decoration: none;">static axisymmetric solution of </ins>the <ins style="font-weight: bold; text-decoration: none;">Einstein vacuum field equations </ins><<ins style="font-weight: bold; text-decoration: none;">math</ins>><ins style="font-weight: bold; text-decoration: none;">R_{\mu\nu} = 0</ins><<ins style="font-weight: bold; text-decoration: none;">/math</ins>> <ins style="font-weight: bold; text-decoration: none;">discovered by [[Hermann Weyl]]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==External links==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* [http://www.rqgravity</ins>.<ins style="font-weight: bold; text-decoration: none;">net/GeneralRelativity#StationaryObservers Concepts </ins>of <ins style="font-weight: bold; text-decoration: none;">General Relativity ] - A first principles demonstration </ins>of <ins style="font-weight: bold; text-decoration: none;">the metric </ins>in <ins style="font-weight: bold; text-decoration: none;">static spacetime</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* [http://arxiv.org/abs/math/0406332v2 M</ins>. <ins style="font-weight: bold; text-decoration: none;">Sanchez</ins>, <ins style="font-weight: bold; text-decoration: none;">On the geometry of static space-times</ins>, <ins style="font-weight: bold; text-decoration: none;">preprint</ins>, <ins style="font-weight: bold; text-decoration: none;">2004</ins>.<ins style="font-weight: bold; text-decoration: none;">]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{{relativity-stub}}</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Lorentzian manifolds]]</ins></div></td></tr>
</table>
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