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Тензор Эйнштейна — Википедия

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width:3.921ex; height:2.843ex;" alt="{\displaystyle G_{\mu \nu }}" /></span>)&#160;— <a href="/wiki/%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80" title="Тензор">тензорная</a> величина, представляющая собой <a href="/wiki/%D0%92%D0%B0%D1%80%D0%B8%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%BD%D0%BE%D0%B5_%D0%B8%D1%81%D1%87%D0%B8%D1%81%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5#Вариационная_производная" title="Вариационное исчисление">вариационную производную</a> <a href="/wiki/%D0%A1%D0%BA%D0%B0%D0%BB%D1%8F%D1%80%D0%BD%D0%B0%D1%8F_%D0%BA%D1%80%D0%B8%D0%B2%D0%B8%D0%B7%D0%BD%D0%B0" title="Скалярная кривизна">скалярной кривизны</a> <a href="/wiki/%D0%A1%D0%B2%D1%8F%D0%B7%D0%BD%D0%BE%D1%81%D1%82%D1%8C_%D0%9B%D0%B5%D0%B2%D0%B8-%D0%A7%D0%B8%D0%B2%D0%B8%D1%82%D1%8B" title="Связность Леви-Чивиты">связности Леви-Чивиты</a> по <a href="/wiki/%D0%9C%D0%B5%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B9_%D1%82%D0%B5%D0%BD%D0%B7%D0%BE%D1%80" title="Метрический тензор">метрическому тензору</a>. В этом качестве стоит в левой части <a href="/wiki/%D0%A3%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D1%8F_%D0%AD%D0%B9%D0%BD%D1%88%D1%82%D0%B5%D0%B9%D0%BD%D0%B0" title="Уравнения Эйнштейна">уравнения Эйнштейна</a>. Тензор Эйнштейна&#160;— симметричный тензор второго ранга в <i>n</i>-мерном пространстве, то есть содержит <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(n+1)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(n+1)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/880739d44f2dc75cf0c9404a2d4b984f1fbc610a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.926ex; height:2.843ex;" alt="{\displaystyle n(n+1)/2}" /></span> независимых компонентов, представляющих собой сложные комбинации компонент метрического тензора и его первых и вторых производных. </p><p>Тензор Эйнштейна равен разности <a href="/wiki/%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80_%D0%A0%D0%B8%D1%87%D1%87%D0%B8" title="Тензор Риччи">тензора Риччи</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\mu \nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>&#x3bc;<!-- μ --></mi> <mi>&#x3bd;<!-- ν --></mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\mu \nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5ee22d1a052bee0115efb8b5ffdaf10b04e42aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.859ex; height:2.843ex;" alt="{\displaystyle R_{\mu \nu }}" /></span> и половины <a href="/wiki/%D0%9C%D0%B5%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B9_%D1%82%D0%B5%D0%BD%D0%B7%D0%BE%D1%80" title="Метрический тензор">метрического тензора</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g_{\mu \nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>&#x3bc;<!-- μ --></mi> <mi>&#x3bd;<!-- ν --></mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g_{\mu \nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5bf4140993a891f5782167dc8a0c236dc7667b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.204ex; height:2.343ex;" alt="{\displaystyle g_{\mu \nu }}" /></span>, умноженного на <a href="/wiki/%D0%A1%D0%BA%D0%B0%D0%BB%D1%8F%D1%80%D0%BD%D0%B0%D1%8F_%D0%BA%D1%80%D0%B8%D0%B2%D0%B8%D0%B7%D0%BD%D0%B0" title="Скалярная кривизна">скалярную кривизну</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}" /></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{\mu \nu }\,=R_{\mu \nu }-{\frac {1}{2}}\,g_{\mu \nu }\,R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>&#x3bc;<!-- μ --></mi> <mi>&#x3bd;<!-- ν --></mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mo>=</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>&#x3bc;<!-- μ --></mi> <mi>&#x3bd;<!-- ν --></mi> </mrow> </msub> <mo>&#x2212;<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>&#x3bc;<!-- μ --></mi> <mi>&#x3bd;<!-- ν --></mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G_{\mu \nu }\,=R_{\mu \nu }-{\frac {1}{2}}\,g_{\mu \nu }\,R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b6001c76a39cb4816cdef7da2c7462554cf1230" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.846ex; height:5.176ex;" alt="{\displaystyle G_{\mu \nu }\,=R_{\mu \nu }-{\frac {1}{2}}\,g_{\mu \nu }\,R}" /></span>.</dd></dl> <p>Домножив обе части этого равенства на <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g^{\mu \nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>&#x3bc;<!-- μ --></mi> <mi>&#x3bd;<!-- ν --></mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g^{\mu \nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55a5070ab85fb1f8797a669a98003bcfcc62182d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.213ex; height:2.676ex;" alt="{\displaystyle g^{\mu \nu }}" /></span> и произведя свёртку, находим <a href="/wiki/%D0%A1%D0%BB%D0%B5%D0%B4_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%86%D1%8B" title="След матрицы">след</a> тензора Эйнштейна: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {Tr} \,G_{\mu \nu }\,={\frac {2\,-n}{2}}\,R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Tr</mi> <mspace width="thinmathspace"></mspace> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>&#x3bc;<!-- μ --></mi> <mi>&#x3bd;<!-- ν --></mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mspace width="thinmathspace"></mspace> <mo>&#x2212;<!-- − --></mo> <mi>n</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {Tr} \,G_{\mu \nu }\,={\frac {2\,-n}{2}}\,R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b08498ed955ef4a53009662d11db8027aaf52b97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.543ex; height:5.176ex;" alt="{\displaystyle \operatorname {Tr} \,G_{\mu \nu }\,={\frac {2\,-n}{2}}\,R}" /></span>.</dd></dl> <p>При этом в частном случае четырёхмерного пространства: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {Tr} \,G_{\mu \nu }\,=-\,R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Tr</mi> <mspace width="thinmathspace"></mspace> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>&#x3bc;<!-- μ --></mi> <mi>&#x3bd;<!-- ν --></mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mo>=</mo> <mo>&#x2212;<!-- − --></mo> <mspace width="thinmathspace"></mspace> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {Tr} \,G_{\mu \nu }\,=-\,R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e7843f235518d1e24a9e8b796a8a6be2fde2b9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.73ex; height:2.843ex;" alt="{\displaystyle \operatorname {Tr} \,G_{\mu \nu }\,=-\,R}" /></span>.</dd></dl> <p>Ковариантная дивергенция тензора Эйнштейна тождественно равна нулю </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{\nu ;\mu }^{\mu }\equiv 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>&#x3bd;<!-- ν --></mi> <mo>;</mo> <mi>&#x3bc;<!-- μ --></mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>&#x3bc;<!-- μ --></mi> </mrow> </msubsup> <mo>&#x2261;<!-- ≡ --></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G_{\nu ;\mu }^{\mu }\equiv 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/840eac9341d28c9d037c64aed0de9b7247a6a89a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.64ex; height:3.176ex;" alt="{\displaystyle G_{\nu ;\mu }^{\mu }\equiv 0}" /></span>,</dd></dl> <p>что служит обоснованием его использования в левой части <a href="/wiki/%D0%A3%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D1%8F_%D0%AD%D0%B9%D0%BD%D1%88%D1%82%D0%B5%D0%B9%D0%BD%D0%B0" title="Уравнения Эйнштейна">уравнения Эйнштейна</a>, так как такое же свойство выполняется для <a href="/wiki/%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D0%B8-%D0%B8%D0%BC%D0%BF%D1%83%D0%BB%D1%8C%D1%81%D0%B0" title="Тензор энергии-импульса">тензора энергии-импульса</a>. </p> <div class="mw-heading mw-heading2"><h2 id="См._также"><span id=".D0.A1.D0.BC._.D1.82.D0.B0.D0.BA.D0.B6.D0.B5"></span>См. также</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80_%D0%AD%D0%B9%D0%BD%D1%88%D1%82%D0%B5%D0%B9%D0%BD%D0%B0&amp;veaction=edit&amp;section=1" title="Редактировать раздел «См. также»" class="mw-editsection-visualeditor"><span>править</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80_%D0%AD%D0%B9%D0%BD%D1%88%D1%82%D0%B5%D0%B9%D0%BD%D0%B0&amp;action=edit&amp;section=1" title="Редактировать код раздела «См. также»"><span>править код</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D1%84%D0%BE%D1%80%D0%BC%D1%83%D0%BB%D0%B8%D1%80%D0%BE%D0%B2%D0%BA%D0%B0_%D0%BE%D0%B1%D1%89%D0%B5%D0%B9_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D0%B8_%D0%BE%D1%82%D0%BD%D0%BE%D1%81%D0%B8%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D0%B8" title="Математическая формулировка общей теории относительности">Математическая формулировка общей теории относительности</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Литература"><span id=".D0.9B.D0.B8.D1.82.D0.B5.D1.80.D0.B0.D1.82.D1.83.D1.80.D0.B0"></span>Литература</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80_%D0%AD%D0%B9%D0%BD%D1%88%D1%82%D0%B5%D0%B9%D0%BD%D0%B0&amp;veaction=edit&amp;section=2" title="Редактировать раздел «Литература»" class="mw-editsection-visualeditor"><span>править</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80_%D0%AD%D0%B9%D0%BD%D1%88%D1%82%D0%B5%D0%B9%D0%BD%D0%B0&amp;action=edit&amp;section=2" title="Редактировать код раздела «Литература»"><span>править код</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="citation" id="CITEREFOhanian1994"><span class="citation"><i>Ohanian, Hans C.</i>&#32;Gravitation and Spacetime&#160;/ Hans C.&#160;Ohanian, Remo Ruffini.&#160;— Second.&#160;— <a href="/wiki/W._W._Norton_%26_Company" title="W. W. Norton &amp; Company">W. W. Norton &amp; Company</a>, 1994.&#160;— <a href="/wiki/%D0%A1%D0%BB%D1%83%D0%B6%D0%B5%D0%B1%D0%BD%D0%B0%D1%8F:%D0%98%D1%81%D1%82%D0%BE%D1%87%D0%BD%D0%B8%D0%BA%D0%B8_%D0%BA%D0%BD%D0%B8%D0%B3/9780393965018" class="internal mw-magiclink-isbn">ISBN 978-0-393-96501-8</a>.</span></span></li> <li><span class="citation" id="CITEREFMartin1995"><span class="citation"><i>Martin, John Legat.</i>&#32;General Relativity: A First Course for Physicists.&#160;— Revised.&#160;— <a href="/wiki/Prentice_Hall" title="Prentice Hall">Prentice Hall</a>, 1995.&#160;— <a href="/wiki/%D0%A1%D0%BB%D1%83%D0%B6%D0%B5%D0%B1%D0%BD%D0%B0%D1%8F:%D0%98%D1%81%D1%82%D0%BE%D1%87%D0%BD%D0%B8%D0%BA%D0%B8_%D0%BA%D0%BD%D0%B8%D0%B3/9780132911962" class="internal mw-magiclink-isbn">ISBN 978-0-13-291196-2</a>.</span></span></li></ul></div><!--esi <esi:include src="/esitest-fa8a495983347898/content" /> --><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&amp;type=1x1&amp;usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Источник — <a dir="ltr" href="https://ru.wikipedia.org/w/index.php?title=Тензор_Эйнштейна&amp;oldid=122013451">https://ru.wikipedia.org/w/index.php?title=Тензор_Эйнштейна&amp;oldid=122013451</a></div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%D0%A1%D0%BB%D1%83%D0%B6%D0%B5%D0%B1%D0%BD%D0%B0%D1%8F:%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D0%B8" title="Служебная:Категории">Категории</a>: <ul><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%8F:%D0%9E%D0%B1%D1%8A%D0%B5%D0%BA%D1%82%D1%8B,_%D0%BD%D0%B0%D0%B7%D0%B2%D0%B0%D0%BD%D0%BD%D1%8B%D0%B5_%D0%B2_%D1%87%D0%B5%D1%81%D1%82%D1%8C_%D0%90%D0%BB%D1%8C%D0%B1%D0%B5%D1%80%D1%82%D0%B0_%D0%AD%D0%B9%D0%BD%D1%88%D1%82%D0%B5%D0%B9%D0%BD%D0%B0" title="Категория:Объекты, названные в честь Альберта Эйнштейна">Объекты, названные в честь Альберта Эйнштейна</a></li><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%8F:%D0%9E%D0%B1%D1%89%D0%B0%D1%8F_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BE%D1%82%D0%BD%D0%BE%D1%81%D0%B8%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D0%B8" title="Категория:Общая теория относительности">Общая теория относительности</a></li><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%8F:%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80%D1%8B_%D0%B2_%D0%9E%D0%A2%D0%9E" title="Категория:Тензоры в ОТО">Тензоры в ОТО</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Скрытая категория: <ul><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%8F:%D0%A1%D1%82%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D1%8B,_%D0%B8%D1%81%D0%BF%D0%BE%D0%BB%D1%8C%D0%B7%D1%83%D1%8E%D1%89%D0%B8%D0%B5_%D0%B2%D0%BE%D0%BB%D1%88%D0%B5%D0%B1%D0%BD%D1%8B%D0%B5_%D1%81%D1%81%D1%8B%D0%BB%D0%BA%D0%B8_ISBN" title="Категория:Страницы, использующие волшебные ссылки ISBN">Страницы, использующие волшебные ссылки ISBN</a></li></ul></div></div> </div> </div> <div id="mw-navigation"> <h2>Навигация</h2> <div id="mw-head"> <nav id="p-personal" class="mw-portlet mw-portlet-personal vector-user-menu-legacy vector-menu" aria-labelledby="p-personal-label" > <h3 id="p-personal-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Персональные инструменты</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anonuserpage" class="mw-list-item"><span title="Страница участника для моего IP">Вы не представились системе</span></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BB%D1%83%D0%B6%D0%B5%D0%B1%D0%BD%D0%B0%D1%8F:%D0%9C%D0%BE%D1%91_%D0%BE%D0%B1%D1%81%D1%83%D0%B6%D0%B4%D0%B5%D0%BD%D0%B8%D0%B5" title="Страница обсуждений для моего IP [n]" accesskey="n"><span>Обсуждение</span></a></li><li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BB%D1%83%D0%B6%D0%B5%D0%B1%D0%BD%D0%B0%D1%8F:%D0%9C%D0%BE%D0%B9_%D0%B2%D0%BA%D0%BB%D0%B0%D0%B4" title="Список правок, сделанных с этого IP-адреса [y]" accesskey="y"><span>Вклад</span></a></li><li id="pt-createaccount" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BB%D1%83%D0%B6%D0%B5%D0%B1%D0%BD%D0%B0%D1%8F:%D0%A1%D0%BE%D0%B7%D0%B4%D0%B0%D1%82%D1%8C_%D1%83%D1%87%D1%91%D1%82%D0%BD%D1%83%D1%8E_%D0%B7%D0%B0%D0%BF%D0%B8%D1%81%D1%8C&amp;returnto=%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80+%D0%AD%D0%B9%D0%BD%D1%88%D1%82%D0%B5%D0%B9%D0%BD%D0%B0" title="Мы предлагаем вам создать учётную запись и войти в систему, хотя это и не обязательно."><span>Создать учётную запись</span></a></li><li id="pt-login" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BB%D1%83%D0%B6%D0%B5%D0%B1%D0%BD%D0%B0%D1%8F:%D0%92%D1%85%D0%BE%D0%B4&amp;returnto=%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80+%D0%AD%D0%B9%D0%BD%D1%88%D1%82%D0%B5%D0%B9%D0%BD%D0%B0" title="Здесь можно зарегистрироваться в системе, но это необязательно. 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href="/w/index.php?title=%D0%A1%D0%BB%D1%83%D0%B6%D0%B5%D0%B1%D0%BD%D0%B0%D1%8F:QrCode&amp;url=https%3A%2F%2Fru.wikipedia.org%2Fwiki%2F%25D0%25A2%25D0%25B5%25D0%25BD%25D0%25B7%25D0%25BE%25D1%2580_%25D0%25AD%25D0%25B9%25D0%25BD%25D1%2588%25D1%2582%25D0%25B5%25D0%25B9%25D0%25BD%25D0%25B0"><span>Скачать QR-код</span></a></li> </ul> </div> </nav> <nav id="p-coll-print_export" class="mw-portlet mw-portlet-coll-print_export vector-menu-portal portal vector-menu" aria-labelledby="p-coll-print_export-label" > <h3 id="p-coll-print_export-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Печать/экспорт</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BB%D1%83%D0%B6%D0%B5%D0%B1%D0%BD%D0%B0%D1%8F:DownloadAsPdf&amp;page=%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80_%D0%AD%D0%B9%D0%BD%D1%88%D1%82%D0%B5%D0%B9%D0%BD%D0%B0&amp;action=show-download-screen" title="Скачать эту страницу как файл PDF"><span>Скачать как PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80_%D0%AD%D0%B9%D0%BD%D1%88%D1%82%D0%B5%D0%B9%D0%BD%D0%B0&amp;printable=yes" title="Версия этой страницы для печати [p]" accesskey="p"><span>Версия для печати</span></a></li> </ul> </div> </nav> <nav id="p-wikibase-otherprojects" class="mw-portlet mw-portlet-wikibase-otherprojects vector-menu-portal portal vector-menu" aria-labelledby="p-wikibase-otherprojects-label" > <h3 id="p-wikibase-otherprojects-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">В других проектах</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q550929" title="Ссылка на связанный элемент репозитория данных [g]" accesskey="g"><span>Элемент Викиданных</span></a></li> </ul> </div> </nav> <nav id="p-lang" class="mw-portlet mw-portlet-lang vector-menu-portal portal vector-menu" aria-labelledby="p-lang-label" > <h3 id="p-lang-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">На других языках</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Tensor_d%27Einstein" title="Tensor d&#039;Einstein — каталанский" lang="ca" hreflang="ca" data-title="Tensor d&#039;Einstein" data-language-autonym="Català" data-language-local-name="каталанский" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Einstein%C5%AFv_tenzor" title="Einsteinův tenzor — чешский" lang="cs" hreflang="cs" data-title="Einsteinův tenzor" data-language-autonym="Čeština" data-language-local-name="чешский" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Einsteintensor" title="Einsteintensor — немецкий" lang="de" hreflang="de" data-title="Einsteintensor" data-language-autonym="Deutsch" data-language-local-name="немецкий" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Einstein_tensor" title="Einstein tensor — английский" lang="en" hreflang="en" data-title="Einstein tensor" data-language-autonym="English" data-language-local-name="английский" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Tensor_de_Einstein" title="Tensor de Einstein — испанский" lang="es" hreflang="es" data-title="Tensor de Einstein" data-language-autonym="Español" data-language-local-name="испанский" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Einsteinen_tentsore" title="Einsteinen tentsore — баскский" lang="eu" hreflang="eu" data-title="Einsteinen tentsore" data-language-autonym="Euskara" data-language-local-name="баскский" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%A7%D9%86%D8%B3%D9%88%D8%B1_%D8%A7%DB%8C%D9%86%D8%B4%D8%AA%DB%8C%D9%86" title="تانسور اینشتین — персидский" lang="fa" hreflang="fa" data-title="تانسور اینشتین" data-language-autonym="فارسی" data-language-local-name="персидский" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Tenseur_d%27Einstein" title="Tenseur d&#039;Einstein — французский" lang="fr" hreflang="fr" data-title="Tenseur d&#039;Einstein" data-language-autonym="Français" data-language-local-name="французский" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%98%D7%A0%D7%96%D7%95%D7%A8_%D7%90%D7%99%D7%99%D7%A0%D7%A9%D7%98%D7%99%D7%99%D7%9F" title="טנזור איינשטיין — иврит" lang="he" hreflang="he" data-title="טנזור איינשטיין" data-language-autonym="עברית" data-language-local-name="иврит" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Einstein-tenzor" title="Einstein-tenzor — венгерский" lang="hu" hreflang="hu" data-title="Einstein-tenzor" data-language-autonym="Magyar" data-language-local-name="венгерский" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Tensore_di_Einstein" title="Tensore di Einstein — итальянский" lang="it" hreflang="it" data-title="Tensore di Einstein" data-language-autonym="Italiano" data-language-local-name="итальянский" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A2%E3%82%A4%E3%83%B3%E3%82%B7%E3%83%A5%E3%82%BF%E3%82%A4%E3%83%B3%E3%83%86%E3%83%B3%E3%82%BD%E3%83%AB" title="アインシュタインテンソル — японский" lang="ja" hreflang="ja" data-title="アインシュタインテンソル" data-language-autonym="日本語" data-language-local-name="японский" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%95%84%EC%9D%B8%EC%8A%88%ED%83%80%EC%9D%B8_%ED%85%90%EC%84%9C" title="아인슈타인 텐서 — корейский" lang="ko" hreflang="ko" data-title="아인슈타인 텐서" data-language-autonym="한국어" data-language-local-name="корейский" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Einstein-tensor" title="Einstein-tensor — нидерландский" lang="nl" hreflang="nl" data-title="Einstein-tensor" data-language-autonym="Nederlands" data-language-local-name="нидерландский" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Tensor_de_Einstein" title="Tensor de Einstein — португальский" lang="pt" hreflang="pt" data-title="Tensor de Einstein" data-language-autonym="Português" data-language-local-name="португальский" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Tensor_ni_Einstein" title="Tensor ni Einstein — тагалог" lang="tl" hreflang="tl" data-title="Tensor ni Einstein" data-language-autonym="Tagalog" data-language-local-name="тагалог" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Einstein_tens%C3%B6r%C3%BC" title="Einstein tensörü — турецкий" lang="tr" hreflang="tr" data-title="Einstein tensörü" data-language-autonym="Türkçe" data-language-local-name="турецкий" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80_%D0%95%D0%B9%D0%BD%D1%88%D1%82%D0%B5%D0%B9%D0%BD%D0%B0" title="Тензор Ейнштейна — украинский" lang="uk" hreflang="uk" data-title="Тензор Ейнштейна" data-language-autonym="Українська" data-language-local-name="украинский" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Tenx%C6%A1_Einstein" title="Tenxơ Einstein — вьетнамский" lang="vi" hreflang="vi" data-title="Tenxơ Einstein" data-language-autonym="Tiếng Việt" data-language-local-name="вьетнамский" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%88%B1%E5%9B%A0%E6%96%AF%E5%9D%A6%E5%BC%A0%E9%87%8F" title="爱因斯坦张量 — китайский" lang="zh" hreflang="zh" data-title="爱因斯坦张量" data-language-autonym="中文" data-language-local-name="китайский" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q550929#sitelinks-wikipedia" title="Править ссылки на другие языки" class="wbc-editpage">Править ссылки</a></span></div> </div> </nav> </div> </div> <footer id="footer" class="mw-footer" > <ul 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