@prefix rdf: . @prefix dbpedia: . @prefix ns2: . dbpedia:Einstein_field_equations rdf:type ns2:PartialDifferentialEquations . @prefix owl: . dbpedia:Einstein_field_equations owl:sameAs . @prefix foaf: . @prefix ns5: . dbpedia:Einstein_field_equations foaf:page ns5:Einstein_field_equations . @prefix dbpprop: . dbpedia:Einstein_field_equations dbpprop:reference , , . @prefix rdfs: . dbpedia:Einstein_field_equations rdfs:label "Ecuaci\u00F3n del campo de Einstein"@es , "Einstein-vergelijkingen"@nl , "Einstein alan denklemleri"@tr , "\u0423\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F \u042D\u0439\u043D\u0448\u0442\u0435\u0439\u043D\u0430"@ru , "R\u00F3wnanie Einsteina"@pl , "Ecua\u0163iile lui Einstein"@ro , "\u00C9quation d'Einstein"@fr , "\u0420\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0415\u0439\u043D\u0448\u0442\u0435\u0439\u043D\u0430"@uk , "Einsteins feltligninger"@no , "Einstein field equations"@en , "Equa\u00E7\u00F5es de campo de Einstein"@pt , "\u30A2\u30A4\u30F3\u30B7\u30E5\u30BF\u30A4\u30F3\u65B9\u7A0B\u5F0F"@ja , "Einsteinsche Feldgleichungen"@de , "Einsteinin kentt\u00E4yht\u00E4l\u00F6t"@fi , "Equacions de camp d'Einstein"@ca , "Equazione di campo di Einstein"@it , "\u7231\u56E0\u65AF\u5766\u573A\u65B9\u7A0B"@zh ; dbpprop:abstract "De Einstein-vergelijkingen zijn een set van vergelijkingen die de algemene relativiteitstheorie van Einstein samenvatten. Net zoals Newton zijn zwaartekrachtstheorie zeer bondig en concreet samenvatte in essentieel \u00E9\u00E9n formule, de Gravitatiewet van Newton, zijn de Einstein-vergelijkingen een concrete wiskundige uitdrukking van Einsteins gehele relativiteitstheorie."@nl , "R\u00F3wnanie Einsteina to r\u00F3wnanie pola og\u00F3lnej teorii wzgl\u0119dno\u015Bci. R\u00F3wnanie Einsteina zwane czasem r\u00F3wnaniem pola grawitacyjnego ma nast\u0119puj\u0105c\u0105 posta\u0107: <math>R_{\\mu \\nu} - \\frac{1}{2} g_{\\mu \\nu} R + \\Lambda g_{\\mu \\nu} = - \\frac{8 \\pi}{c^4} G T_{\\mu \\nu}</math> gdzie: <math>R_{\\mu \\nu}</math> - tensor krzywizny Ricciego, <math>R</math> - skalar krzywizny Ricciego, <math>g_{\\mu \\nu}</math> - tensor metryczny, <math>\\Lambda</math> - sta\u0142a kosmologiczna, <math>T_{\\mu \\nu}</math> - tensor energii-p\u0119du, <math>\\pi</math> - liczba pi, c - pr\u0119dko\u015B\u0107 \u015Bwiat\u0142a w pr\u00F3\u017Cni, G - sta\u0142a grawitacji. Natomiast <math>g_{\\mu \\nu}</math> opisuje metryk\u0119 rozmaito\u015Bci i jest tensorem symetrycznym 4 x 4, ma wi\u0119c 10 niezale\u017Cnych sk\u0142adowych. Jest to r\u00F3wnanie tensorowe, jednak rozbijaj\u0105c tensor na sk\u0142adowe mo\u017Cna otrzyma\u0107 z niego uk\u0142ad r\u00F3wna\u0144 liczbowych. Bior\u0105c pod uwag\u0119 dowolno\u015B\u0107 przy wyborze czterech wsp\u00F3\u0142rz\u0119dnych czasoprzestrzennych, liczba niezale\u017Cnych r\u00F3wna\u0144 wynosi 6. Powy\u017Csza posta\u0107 r\u00F3wnania przedstawiona jest przy u\u017Cyciu konwencji znak\u00F3w tensora metrycznego (+---) stosowanej cz\u0119sto w polskiej literaturze. Konwencja ta nie jest jedyn\u0105 mo\u017Cliw\u0105. Spotyka si\u0119 czasem (np. w angielskiej wikipedii) zapis przy u\u017Cyciu alternatywnej konwencji (-+++), co prowadzi do zmiany znaku prawej strony r\u00F3wnania. R\u00F3wnanie Einsteina mo\u017Cna rozumie\u0107 jako r\u00F3wnanie na tensor metryczny <math>g_{\\mu\\nu}</math> kt\u00F3ry jest okre\u015Blony poprzez rozk\u0142ad materii i energii zawarty w tensorze energii-p\u0119du. Pomimo z pozoru prostego wygl\u0105du r\u00F3wnanie Einsteina jest bardzo skomplikowane. Spowodowane jest to z\u0142o\u017Con\u0105 i nieliniow\u0105 zale\u017Cno\u015Bci\u0105 tensora i skalara krzywizny Ricciego od tensora metrycznego. W konsekwencji r\u00F3wnanie Einsteina zosta\u0142o rozwi\u0105zane jedynie w nielicznych przypadkach - np. dla uk\u0142ad\u00F3w o sferycznie-symetrycznym rozk\u0142adzie masy. W zastosowaniach astrofizycznych (ale nie kosmologicznych) sta\u0142\u0105 kosmologiczn\u0105 mo\u017Cna zaniedba\u0107. R\u00F3wnanie Einsteina bez sta\u0142ej kosmologicznej mo\u017Cna zapisa\u0107 w bardziej zwartej postaci definiuj\u0105c tensor Einsteina: <math>G_{\\mu\\nu}=R_{\\mu\\nu}-\\frac{1}{2}Rg_{\\mu\\nu}</math> kt\u00F3ry jest symetrycznym tensorem drugiego rz\u0119du b\u0119d\u0105cym funkcj\u0105 tensora metrycznego <math>g_{\\mu\\nu}</math>. Przechodz\u0105c do jednostek geometrycznych, gdzie <math>G=c=1</math>, otrzymamy r\u00F3wnanie Einsteina w postaci: <math>G_{\\mu\\nu}=-8\\pi T_{\\mu\\nu}</math>. Lewa strona r\u00F3wnania reprezentuje krzywizn\u0119 czasoprzestrzeni okre\u015Blon\u0105 tensorem metrycznym. Prawa strona natomiast opisuje materi\u0119 i energi\u0119 wype\u0142niaj\u0105c\u0105 czasoprzestrze\u0144. Tak wi\u0119c pomimo z\u0142o\u017Conej szczeg\u00F3\u0142owej formy matematycznej fundamentalne znaczenie r\u00F3wnania Einsteina mo\u017Cna zamkn\u0105\u0107 w stwierdzeniu: rozk\u0142ad materii i energii w czasoprzestrzeni wprost i jednoznacznie okre\u015Bla jej krzywizn\u0119. Rozk\u0142ad materii i energii w czasoprzestrzeni opisywana jest przez tensor energii-p\u0119du. Ka\u017Cda z jego sk\u0142adowych okre\u015Bla strumie\u0144 p\u0119du na jednostk\u0119 obj\u0119to\u015Bci przestrzeni. Sk\u0142adowa 0,0 oznacza np. g\u0119sto\u015B\u0107 masy. W zastosowaniach kosmologicznych mo\u017Cna przyj\u0105\u0107 przybli\u017Cony wz\u00F3r: <math>T_{\\mu \\nu}=(\\epsilon+P)u_{\\mu}u_{\\nu}-g_{\\mu \\nu}P</math> gdzie u jest wektorem jednostkowym <math>u_{\\mu}u^{\\mu}=1</math>, <math>\\epsilon</math> jest przestrzennym rozk\u0142adem energii a P rozk\u0142adem ci\u015Bnienia. Wraz z r\u00F3wnaniem geodezyjnych, r\u00F3wnanie Einsteina stanowi podstaw\u0119 matematycznego sformu\u0142owania Og\u00F3lnej Teorii Wzgl\u0119dno\u015Bci."@pl , "\u0420\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0415\u0439\u043D\u0448\u0442\u0435\u0439\u043D\u0430 - \u043E\u0441\u043D\u043E\u0432\u043D\u0456 \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0437\u0430\u0433\u0430\u043B\u044C\u043D\u043E\u0457 \u0442\u0435\u043E\u0440\u0456\u0457 \u0432\u0456\u0434\u043D\u043E\u0441\u043D\u043E\u0441\u0442\u0456. \u041D\u0435\u0432\u0456\u0434\u043E\u043C\u043E\u044E \u0432\u0435\u043B\u0438\u0447\u0438\u043D\u043E\u044E \u0432 \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F\u0445 \u0415\u0439\u043D\u0448\u0442\u0435\u0439\u043D\u0430 \u0454 \u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0438\u0439 \u0442\u0435\u043D\u0437\u043E\u0440 <math> g_{ik} </math> <math>(1) \\qquad R_{ik} - {1 \\over 2} R g_{ik} + \\Lambda g_{ik} = 8 \\pi {G \\over c^4} T_{ik}</math> \u0434\u0435 <math>R_{ik}</math> \u2014 \u0442\u0435\u043D\u0437\u043E\u0440 \u0420\u0456\u0447\u0447\u0456, <math>R</math> - \u0441\u043A\u0430\u043B\u044F\u0440\u043D\u0435 \u0432\u0438\u043A\u0440\u0438\u0432\u043B\u0435\u043D\u043D\u044F, <math>g_{ik}</math> \u2014 \u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0438\u0439 \u0442\u0435\u043D\u0437\u043E\u0440, <math>\\Lambda</math> - \u043A\u043E\u0441\u043C\u043E\u043B\u043E\u0433\u0456\u0447\u043D\u0430 \u043A\u043E\u043D\u0441\u0442\u0430\u043D\u0442\u0430, <math>T_{ik}</math> \u2014 \u0442\u0435\u043D\u0437\u043E\u0440 \u0435\u043D\u0435\u0440\u0433\u0456\u0457-\u0456\u043C\u043F\u0443\u043B\u044C\u0441\u0443, \u044F\u043A\u0438\u0439 \u0432\u0438\u0437\u043D\u0430\u0447\u0430\u0454 \u043D\u0435\u0433\u0440\u0430\u0432\u0456\u0442\u0443\u044E\u0447\u0443 \u043C\u0430\u0442\u0435\u0440\u0456\u044E, \u0435\u043D\u0435\u0440\u0433\u0456\u044E \u0442\u0430 \u0441\u0438\u043B\u0438 \u0432 \u0434\u043E\u0432\u0456\u043B\u044C\u043D\u0456\u0439 \u0442\u043E\u0447\u0446\u0456 \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0443-\u0447\u0430\u0441\u0443, <math>\\pi</math> \u2014 \u0447\u0438\u0441\u043B\u043E \u043F\u0456, <math>c</math> \u2014 \u0448\u0432\u0438\u0434\u043A\u0456\u0441\u0442\u044C \u0441\u0432\u0456\u0442\u043B\u0430, <math>G</math> \u2014 \u0433\u0440\u0430\u0432\u0456\u0442\u0430\u0446\u0456\u0439\u043D\u0430 \u0441\u0442\u0430\u043B\u0430, \u044F\u043A\u0430 \u0437\u2019\u044F\u0432\u043B\u044F\u0454\u0442\u044C\u0441\u044F \u0456 \u0432 \u0432\u0456\u0434\u043F\u043E\u0432\u0456\u0434\u043D\u043E\u043C\u0443 \u0437\u0430\u043A\u043E\u043D\u0456 \u0432\u0441\u0435\u0441\u0432\u0456\u0442\u043D\u044C\u043E\u0433\u043E \u0442\u044F\u0436\u0456\u043D\u043D\u044F \u041D\u044C\u044E\u0442\u043E\u043D\u0430. \u0422\u0435\u043D\u0437\u043E\u0440 \u0420\u0456\u0447\u0447\u0456, \u0441\u043A\u0430\u043B\u044F\u0440\u043D\u0435 \u0432\u0438\u043A\u0440\u0438\u0432\u043B\u0435\u043D\u043D\u044F \u0442\u0430 \u0442\u0435\u043D\u0437\u043E\u0440 \u0435\u043D\u0435\u0440\u0433\u0456\u0457-\u0456\u043C\u043F\u0443\u043B\u044C\u0441\u0443 \u0442\u0435\u0436 \u0437\u0430\u043B\u0435\u0436\u0430\u0442\u044C \u0432\u0456\u0434 \u043C\u0435\u0442\u0440\u0438\u0447\u043D\u043E\u0433\u043E \u0442\u0435\u043D\u0437\u043E\u0440\u0430. \u0412 \u0437\u0430\u0433\u0430\u043B\u044C\u043D\u043E\u043C\u0443 \u0432\u0438\u043F\u0430\u0434\u043A\u0443 \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0415\u0439\u043D\u0448\u0442\u0435\u0439\u043D\u0430 \u043C\u0456\u0441\u0442\u0438\u0442\u044C \u043A\u043E\u0441\u043C\u043E\u043B\u043E\u0433\u0456\u0447\u043D\u0443 \u043A\u043E\u043D\u0441\u0442\u0430\u043D\u0442\u0443, \u0445\u043E\u0447\u0430 \u043F\u0456\u0437\u043D\u0456\u0448\u0435 \u0415\u0439\u043D\u0448\u0442\u0435\u0439\u043D \u0432\u0456\u0434\u043F\u043C\u043E\u0432\u0438\u0432\u0441\u044F \u0432\u0456\u0434 \u0457\u0457 \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u0430\u043D\u043D\u044F. \u041A\u043E\u0441\u043C\u043E\u043B\u043E\u0433\u0456\u0447\u043D\u0430 \u043A\u043E\u043D\u0441\u0442\u0430\u043D\u0442\u0430 \u0431\u0443\u043B\u0430 \u0437\u0430\u043F\u0440\u043E\u0432\u0430\u0434\u0436\u0435\u043D\u0430 \u0434\u043B\u044F \u0442\u043E\u0433\u043E, \u0449\u043E\u0431 \u0434\u043E\u0441\u044F\u0433\u0442\u0438 \u0441\u0442\u0430\u0446\u0456\u043E\u043D\u0430\u0440\u043D\u043E\u0441\u0442\u0456 \u0412\u0441\u0435\u0441\u0432\u0456\u0442\u0443, \u0430\u043B\u0435 \u0432\u0456\u0434\u043A\u0440\u0438\u0442\u0442\u044F \u0447\u0435\u0440\u0432\u043E\u043D\u043E\u0433\u043E \u0437\u0441\u0443\u0432\u0443 \u0437\u0430\u043A\u043B\u0430\u043B\u043E \u0441\u0443\u043C\u043D\u0456\u0432\u0438 \u0432 \u0441\u0442\u0430\u0446\u0456\u043E\u043D\u0430\u0440\u043D\u043E\u0441\u0442\u0456. \u0406\u043D\u0444\u043E\u0440\u043C\u0430\u0446\u0456\u044F \u043F\u0440\u043E \u0440\u043E\u0437\u043F\u043E\u0434\u0456\u043B \u043C\u0430\u0441 \u0456 \u043F\u043E\u043B\u0456\u0432 \u043C\u0456\u0441\u0442\u0438\u0442\u044C\u0441\u044F \u0432 \u0442\u0435\u043D\u0437\u043E\u0440\u0456 \u0435\u043D\u0435\u0440\u0433\u0456\u0457-\u0456\u043C\u043F\u0443\u043B\u044C\u0441\u0443. \u0414\u043B\u044F \u043F\u043E\u0432\u043D\u043E\u0433\u043E \u0440\u043E\u0437\u0433\u043B\u044F\u0434\u0443 \u0444\u0456\u0437\u0438\u0447\u043D\u043E\u0457 \u0441\u0438\u0441\u0442\u0435\u043C\u0438 \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0415\u0439\u043D\u0448\u0442\u0435\u0439\u043D\u0430 \u043F\u043E\u0432\u0438\u043D\u043D\u0456 \u0431\u0443\u0442\u0438 \u0434\u043E\u043F\u043E\u0432\u043D\u0435\u043D\u0438\u043C\u0438 \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F\u043C \u0441\u0442\u0430\u043D\u0443 \u043C\u0430\u0442\u0435\u0440\u0456\u0457."@uk , "L'equazione di campo di Einstein \u00E8 il risultato finale della teoria della relativit\u00E0 generale, sviluppata da Albert Einstein nel 1915. \u00C8 stata al centro di una polemica di priorit\u00E0 tra lo stesso Einstein ed il matematico David Hilbert, risolta solo recentemente a favore di Einstein. In breve, le equazioni di campo di Einstein descrivono la curvatura dello spaziotempo, in funzione della densit\u00E0 di materia, dell'energia e della pressione, rappresentate tramite il tensore stress-energia T. Nella forma con la costante cosmologica, l'equazione di campo \u00E8 <math>R_{\\mu \\nu} - {1 \\over 2} g_{\\mu \\nu} R + \\Lambda g_{\\mu \\nu} = \\frac{8 \\pi G}{c^4} T_{\\mu \\nu}</math> dove: <math>R_{\\mu \\nu}</math>: tensore di curvatura di Ricci, <math>R</math>: curvatura scalare, cio\u00E8 la traccia di <math>R_{\\mu \\nu}</math> <math>g_{\\mu \\nu}</math>: tensore metrico, <math>\\Lambda</math>: costante cosmologica, <math>T_{\\mu \\nu}</math>: tensore stress-energia, <math>c</math>: velocit\u00E0 della luce, <math>G</math>: costante di gravitazione universale. Il tensore <math>g_{\\mu \\nu}</math> descrive la metrica dello spazio-tempo ed \u00E8 un tensore simmetrico 4x4, che quindi ha 10 componenti indipendenti; date le 4 coordinate utilizzate, le equazioni indipendenti si riducono a 6."@it , "Em f\u00EDsica, a equa\u00E7\u00E3o de campo de Einstein ou a equa\u00E7\u00E3o Einstein \u00E9 uma equa\u00E7\u00E3o na teoria da gravita\u00E7\u00E3o, chamada relatividade geral, que descreve como a mat\u00E9ria gera gravidade e, inversamente, como a gravidade afeta a mat\u00E9ria. A equa\u00E7\u00E3o do campo de Einstein se reduz \u00E0 lei de Newton da gravidade no limite n\u00E3o-relativista, isto \u00E9, \u00E0 velocidades baixas e campos gravitacionais pouco intensos. Na equa\u00E7\u00E3o, a gravidade se d\u00E1 em termos de um tensor m\u00E9trico, uma quantidade que descreve as propriedades geom\u00E9tricas do espa\u00E7o-tempo tetradimensional. A mat\u00E9ria \u00E9 descrita por seu tensor de energia-momento, uma quantidade que cont\u00E9m a densidade e a press\u00E3o da mat\u00E9ria. Estes tensores s\u00E3o tensores sim\u00E9tricos 4 x 4, de modo que t\u00EAm 10 componentes independentes. Dada a liberdade de escolha das quatro coordenadas do espa\u00E7o-tempo, as equa\u00E7\u00F5es independentes se reduzem a 6. A for\u00E7a de acoplamento entre a mat\u00E9ria e a gravidade \u00E9 determinada pela constante gravitacional universal."@pt , "\u5F9E\u7B49\u6548\u539F\u7406\uFF081907\u5E74\uFF09\u958B\u59CB\uFF0C\u5230\u5F8C\u4F86\uFF081912\u5E74\u524D\u5F8C\uFF09\u767C\u5C55\u51FA\u300C\u5B87\u5B99\u4E2D\u4E00\u5207\u7269\u8CEA\u7684\u904B\u52D5\u90FD\u53EF\u4EE5\u7528\u66F2\u7387\u4F86\u63CF\u8FF0\uFF0C\u91CD\u529B\u5834\u5BE6\u969B\u4E0A\u662F\u5F4E\u66F2\u6642\u7A7A\u7684\u8868\u73FE\u300D\u7684\u601D\u60F3\uFF0C\u611B\u56E0\u65AF\u5766\u6B77\u7D93\u6F2B\u9577\u7684\u8A66\u8AA4\u904E\u7A0B\uFF0C\u65BC1916\u5E7411\u670825\u65E5\u5BEB\u4E0B\u4E86\u91CD\u529B\u5834\u65B9\u7A0B\u5F0F\u800C\u5B8C\u6210\u5EE3\u7FA9\u76F8\u5C0D\u8AD6\u3002\u9019\u689D\u65B9\u7A0B\u5F0F\u7A31\u4F5C\u611B\u56E0\u65AF\u5766\u91CD\u529B\u5834\u65B9\u7A0B\u5F0F\uFF0C\u6216\u7C21\u70BA\u611B\u56E0\u65AF\u5766\u5834\u65B9\u7A0B\u5F0F\u6216\u611B\u56E0\u65AF\u5766\u65B9\u7A0B\u5F0F\uFF1A <math>G_{\\mu\\nu} = R_{\\mu\\nu} - \\frac{1}{2}g_{\\mu\\nu} R = {8 \\pi G \\over c^4} T_{\\mu\\nu}</math> \u5176\u4E2D <math>G_{\\mu\\nu}\\,</math>\u7A31\u70BA\u611B\u56E0\u65AF\u5766\u5F35\u91CF\uFF0C <math>R_{\\mu\\nu}\\,</math>\u662F\u5F9E\u9ECE\u66FC\u5F35\u91CF\u7E2E\u4F75\u800C\u6210\u7684\u91CC\u5947\u5F35\u91CF\uFF0C\u4EE3\u8868\u66F2\u7387\u9805\uFF1B <math>g_{\\mu\\nu}\\,</math>\u662F\u5F9E(3+1)\u7DAD\u6642\u7A7A\u7684\u5EA6\u91CF\u5F35\u91CF\uFF1B <math>T_{\\mu\\nu}\\,</math>\u662F\u80FD\u91CF-\u52D5\u91CF-\u61C9\u529B\u5F35\u91CF\uFF0C <math>G\\,</math>\u662F\u91CD\u529B\u5E38\u6578\uFF0C <math>c\\,</math>\u662F\u771F\u7A7A\u4E2D\u5149\u901F\u3002 \u8BE5\u65B9\u7A0B\u662F\u4E00\u4E2A\u4EE5\u65F6\u7A7A\u4E3A\u81EA\u53D8\u91CF\u3001\u4EE5\u5EA6\u89C4\u4E3A\u56E0\u53D8\u91CF\u7684\u5E26\u6709\u692D\u5706\u578B\u7EA6\u675F\u7684\u4E8C\u9636\u53CC\u66F2\u578B\u504F\u5FAE\u5206\u65B9\u7A0B\u3002\u7403\u9762\u5BF9\u79F0\u7684\u51C6\u786E\u89E3\u79F0\u53F2\u74E6\u897F\u89E3\u3002"@zh , "Ecua\u0163iile lui Einstein, au fost descoperite de David Hilbert \u015Fi Albert Einstein practic concomitent \u00EEn anul 1915. Ele reprezint\u0103 un sistem de ecua\u0163ii diferen\u0163iale neliniare de gradul 2 din care fac parte tensorii metric, Ricci \u015Fi energie -impuls al sursei, scalarul Ricci. Tensorul Ricci de rang 2 se ob\u0163ine din tensorul antisimetric dup\u0103 perechile de indici de rang 4 Riemann, iar scalarul Ricci se ob\u0163ine de pe urma tensorului Ricci. Aceste ecua\u0163ii fiind rezolvate, cu anumite condi\u0163ii de frontier\u0103, ele permit s\u0103 se ob\u0163in\u0103 solu\u0163ii particulare, care reprezint\u0103 c\u00E2mpul gravita\u0163ional de o simetrie concret\u0103. Exist\u0103 solu\u0163ii statice, sta\u0163ionare, nesta\u0163ionare \u00EEn func\u0163ie de dependen\u0163a sau independen\u0163a de timp \u015Fi de forma acestei dependen\u0163e, solu\u0163ii de simetrie plan\u0103, sferic\u0103, cilindric\u0103, etc. Num\u0103rul solu\u0163iilor cunoscute p\u00E2n\u0103 \u00EEn prezent \u00EEntrece miile, dar cele mai importante sunt solu\u0163ia Schwarzschild, solu\u0163ia ce prezint\u0103 undele gravita\u0163ionale \u015Fi solu\u0163ia cosmologic\u0103 Fridman-Robertson-Walker, care prezint\u0103 Universul."@ro , "Einstein alan denklemleri ya da Einstein denklemleri (k\u0131saca EAD), y\u00FCksek h\u0131z ve b\u00FCy\u00FCk k\u00FCtlelerde ge\u00E7erli olan uzayzaman\u0131n geometrisi ile enerji ve momentum da\u011F\u0131l\u0131m\u0131n\u0131 ili\u015Fkilendiren do\u011Frusal olmayan diferansiyel denklemler k\u00FCmesidir. Einstein, bu denklemleri ilk kez 1915 y\u0131l\u0131nda yay\u0131mlam\u0131\u015Ft\u0131r. Bu denklemler, uzayzaman\u0131n e\u011Frili\u011Fini momentum ve enerji da\u011F\u0131l\u0131m\u0131na e\u015Fde\u011Ferlik ilkesi ile e\u015Fleyen on denklemden olu\u015Fur. Einstein tens\u00F6r\u00FC, metrik tens\u00F6r ile ba\u011F\u0131nt\u0131l\u0131d\u0131r. Bu y\u00FCzden problem, verilen bir enerji momentum da\u011F\u0131l\u0131m\u0131 i\u00E7in metrik tens\u00F6r\u00FCn\u00FC \u00E7\u00F6zmektir. bu denklemler, d\u00FC\u015F\u00FCk h\u0131zlarda ve d\u00FC\u015F\u00FCk k\u00FCtlelerde Newton mekani\u011Fine yak\u0131nsar. Bu denklemler, Genel g\u00F6relilik kuram\u0131 ve \u00F6zel g\u00F6relilik kuram\u0131 olarak iki ana ba\u015Fl\u0131k alt\u0131nda incelenir. Denklemler, k\u00FCtlenin olmad\u0131\u011F\u0131 bir evren i\u00E7in \u00E7\u00F6z\u00FCl\u00FCrse; y\u00E2ni denklemin \u00E2\u015Fik\u00E2r \u00E7\u00F6z\u00FCm\u00FC al\u0131n\u0131rsa \u00F6zel g\u00F6relilik kuram\u0131na ula\u015F\u0131l\u0131r. Bu kuram zaman\u0131n, uzay\u0131n bir par\u00E7as\u0131 oldu\u011Funu ve evrendeki limit h\u0131z\u0131n \u0131\u015F\u0131k h\u0131z\u0131 oldu\u011Funu kan\u0131tlam\u0131\u015Ft\u0131r. Genel g\u00F6relilik kuram\u0131nda ise ivmenin dahil oldu\u011Fu Newton'un k\u00FCtle \u00E7ekim yasas\u0131n\u0131n uzayda e\u011Frilikler yaratt\u0131\u011F\u0131n\u0131 \u00F6ne s\u00FCrm\u00FC\u015F ve bunu da yap\u0131lan deneyler kan\u0131tlam\u0131\u015Ft\u0131r. Einstein alan denklemlerinin \u00E2\u015Fik\u00E2r olmayan tek bir \u00E7\u00F6z\u00FCm\u00FC vard\u0131r. Bu \u00E7\u00F6z\u00FCme Shcwartzshil \u00E7\u00F6z\u00FCm\u00FC denir."@tr , "The Einstein field equations (EFE) or Einstein's equations are a set of ten equations in Einstein's theory of general relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy. First published by Einstein in 1915 as a tensor equation, the EFE equate spacetime curvature (expressed by the Einstein tensor) with the energy and momentum within that spacetime (expressed by the stress-energy tensor). Similar to the way that electromagnetic fields are determined using charges and currents via Maxwell's equations, the EFE are used to determine the spacetime geometry resulting from the presence of mass-energy and linear momentum, that is, they determine the metric tensor of spacetime for a given arrangement of stress-energy in the spacetime. The relationship between the metric tensor and the Einstein tensor allows the EFE to be written as a set of non-linear partial differential equations when used in this way. The solutions of the EFE are the components of the metric tensor. The inertial trajectories of particles and radiation in the resulting geometry are then calculated using the geodesic equation. As well as obeying local energy-momentum conservation, the EFE reduce to Newton's law of gravitation where the gravitational field is weak. Solution techniques for the EFE include simplifying assumptions such as symmetry. Special classes of exact solutions are most often studied as they model many gravitational phenomena, such as rotating black holes and the expanding universe. Further simplification is achieved in approximating the actual spacetime as flat spacetime with a small deviation, leading to the linearised EFE. These equations are used to study phenomena such as gravitational waves."@en , "Relativitat general Fitxer:Neutronstar Light Deflection. png Equacions de camp d'Einstein Equacions de Friedmann Forat negre Gravetat qu\u00E0ntica Horitz\u00F3 d'esdeveniments Lent gravitat\u00F2ria M\u00E8trica d'Schwarzschild M\u00E8trica de Kerr M\u00E8trica FLRW Ona gravitat\u00F2ria Principi d'equival\u00E8ncia Relativitat general Solucions exactes de la RG Univers d'Einstein-De Sitter Temes relacionats Albert Einstein Astrof\u00EDsica Cosmologia Geometria de Riemann Gravetat Les equacions de camp d'Einstein, tamb\u00E9 anomenades simplement equacions d'Einstein o equaci\u00F3 d'Einstein, s\u00F3n el conjunt b\u00E0sic d'equacions de la relativitat general. Descriuen la relaci\u00F3 entre la curvatura de l'espai-temps (expressada amb el tensor d'Einstein) i l'energia i el moment dins l'espai-temps (expressada amb el tensor energia-impuls). En altres paraules, permeten determinar la curvatura de l'espai-temps a partir de la distribuci\u00F3 de masses i energies que hi ha en aquest espai-temps, aix\u00ED com determinar com es desplacen les masses a causa de la mateixa curvatura de l'espai-temps. Aquesta curvatura de l'espai-temps s'interpreta com el camp gravitatori creat per les masses. De forma molt aproximada les equacions d'Einstein tenen l'estructura general: En realitat, per\u00F2, les equacions s\u00F3n un conjunt de deu equacions diferencials no lineals, que es poden agrupar en una sola equaci\u00F3 tensorial. Les equacions de camp es redueixen a la llei de Newton de la gravetat en el l\u00EDmit no relativista (\u00E9s a dir, a velocitats baixes i camps gravitacionals febles)."@ca , "Im Rahmen der allgemeinen Relativit\u00E4tstheorie wird durch die einsteinschen Feldgleichungen, auch Einsteingleichungen, Einstein-Hilbert-Gleichungen oder Gravitationsgleichungen, das physikalische Ph\u00E4nomen der Gravitation klassisch beschrieben. Die Entwicklung der einsteinschen Feldgleichungen basiert auf der Grundidee, die Schwerkraft zu geometrisieren, also alle Eigenschaften der Gravitation und ihrer Wirkung auf physikalische Prozesse mit Hilfe der Eigenschaften eines riemannschen Raumes abzubilden."@de , "\u30A2\u30A4\u30F3\u30B7\u30E5\u30BF\u30A4\u30F3\u65B9\u7A0B\u5F0F\uFF08the Einstein equations\uFF09\u306F\u3001\u30A2\u30EB\u30D9\u30EB\u30C8\u30FB\u30A2\u30A4\u30F3\u30B7\u30E5\u30BF\u30A4\u30F3\u304C1916\u5E74\u306B\u4E00\u822C\u76F8\u5BFE\u6027\u7406\u8AD6\u306E\u4E2D\u3067\u5C0E\u3044\u305F\u3001\u4E07\u6709\u5F15\u529B\u30FB\u91CD\u529B\u5834\u3092\u8A18\u8FF0\u3059\u308B\u5834\u306E\u65B9\u7A0B\u5F0F (Field equation\uFF09\u3067\u3042\u308B\u3002\u30A2\u30A4\u30B6\u30C3\u30AF\u30FB\u30CB\u30E5\u30FC\u30C8\u30F3\u304C\u5C0E\u3044\u305F\u4E07\u6709\u5F15\u529B\u306E\u6CD5\u5247\u3092\u3001\u5F37\u3044\u91CD\u529B\u5834\u306B\u5BFE\u3057\u3066\u9069\u7528\u3067\u304D\u308B\u3088\u3046\u306B\u62E1\u5F35\u3057\u305F\u65B9\u7A0B\u5F0F\u3067\u3042\u308A\u3001\u5BFE\u8C61\u3068\u3059\u308B\u7269\u7406\u7684\u73FE\u8C61\u306F\u4E2D\u6027\u5B50\u661F\u3084\u30D6\u30E9\u30C3\u30AF\u30DB\u30FC\u30EB\u306A\u3069\u306E\u9AD8\u5BC6\u5EA6\u30FB\u5927\u8CEA\u91CF\u5929\u4F53\u3084\u3001\u5B87\u5B99\u5168\u4F53\u306E\u5E7E\u4F55\u5B66\u306A\u3069\u306B\u306A\u308B\u3002\u30A2\u30A4\u30F3\u30B7\u30E5\u30BF\u30A4\u30F3\u306E\u91CD\u529B\u5834\u306E\u65B9\u7A0B\u5F0F\uFF08\u3058\u3085\u3046\u308A\u3087\u304F\u3070\u306E\u307B\u3046\u3066\u3044\u3057\u304D\u3001Einstein's field equations of General Relativity\uFF09\u3068\u3082\u547C\u3070\u308C\u3001\u3053\u306E\u305F\u3081 EFE \u3068\u3082\u7565\u3055\u308C\u308B\u3002\u6982\u7565\u3084\u5C0E\u51FA\u30FB\u5FDC\u7528\u306A\u3069\u306E\u8A73\u3057\u3044\u8AAC\u660E\u306F\u3001\u4E00\u822C\u76F8\u5BFE\u6027\u7406\u8AD6\u306E\u9805\u3092\u53C2\u7167\u306E\u3053\u3068\u3002"@ja , "L'\u00E9quation d'Einstein ou \u00E9quation de champ d'Einstein est l'\u00E9quation aux d\u00E9riv\u00E9es partielles principale de la relativit\u00E9 g\u00E9n\u00E9rale. C'est une \u00E9quation dynamique qui d\u00E9crit comment la mati\u00E8re et l'\u00E9nergie modifient la g\u00E9om\u00E9trie de l'espace-temps. Cette courbure de la g\u00E9om\u00E9trie autour d'une source de mati\u00E8re est alors interpr\u00E9t\u00E9e comme le champ gravitationnel de cette source. Le mouvement des objets dans ce champ est d\u00E9crit tr\u00E8s pr\u00E9cis\u00E9ment par l'\u00E9quation de sa g\u00E9od\u00E9sique."@fr , "Einsteinin kentt\u00E4yht\u00E4l\u00F6t tai Einsteinin yht\u00E4l\u00F6t ovat kymmenen Albert Einsteinin yleisen suhteellisuusteorian yht\u00E4l\u00F6\u00E4, jotka kuvaavat gravitaation massan ja energian aiheuttamana aika-avaruuden kaareutumana. Tarkalleen ottaen kentt\u00E4yht\u00E4l\u00F6t ilmaisevat yhteyden avaruuden geometrian ja siell\u00E4 olevan massan ja energian v\u00E4lill\u00E4."@fi , "Einsteins feltligninger (EFL) er et sett med ti ligninger, redusert fra seksten grunnet symmetri, i Einsteins generelle relativitetsteori som er en teori for gravitasjon. Denne teorien beskriver gravitasjon som en krumning av tidrommet som f\u00F8lge av masse og energi. EFL uttrykker proporsjonalitetsforholdet mellom disse egenskapene. Ligningene ble f\u00F8rst publisert i 1915."@no , "En f\u00EDsica, la ecuaci\u00F3n del campo de Einstein o la ecuaci\u00F3n de Einstein es una ecuaci\u00F3n en la teor\u00EDa de la gravitaci\u00F3n, llamada relatividad general, que describe c\u00F3mo la materia crea gravedad e, inversamente, c\u00F3mo la gravedad afecta la materia. La ecuaci\u00F3n del campo de Einstein se reduce a la ley de Newton de la gravedad en el l\u00EDmite no-relativista, esto es, a velocidades bajas y campos gravitacionales d\u00E9biles. En la ecuaci\u00F3n, la gravedad se da en t\u00E9rminos de un tensor m\u00E9trico, una cantidad que describe las propiedades geom\u00E9tricas del espacio-tiempo tetradimensional. La materia es descrita por su tensor de tensi\u00F3n-energ\u00EDa, una cantidad que contiene la densidad y la presi\u00F3n de la materia. Estos tensores son tensores sim\u00E9tricos 4 x 4, de modo que tienen 10 componentes independientes. Dada la libertad de elecci\u00F3n de las cuatro coordenadas del espacio-tiempo, las ecuaciones independientes se reducen a 6. La fuerza de acoplamiento entre la materia y la gravedad es determinada por la constante gravitatoria universal."@es , "\u0423\u0440\u0430\u0432\u043D\u0435\u0301\u043D\u0438\u044F \u042D\u0439\u043D\u0448\u0442\u0435\u0301\u0439\u043D\u0430 (\u0438\u043D\u043E\u0433\u0434\u0430 \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u0435\u0442\u0441\u044F \u043D\u0430\u0437\u0432\u0430\u043D\u0438\u0435 \u00AB\u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F \u042D\u0439\u043D\u0448\u0442\u0435\u0439\u043D\u0430-\u0413\u0438\u043B\u044C\u0431\u0435\u0440\u0442\u0430\u00BB) \u2014 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F \u0433\u0440\u0430\u0432\u0438\u0442\u0430\u0446\u0438\u043E\u043D\u043D\u043E\u0433\u043E \u043F\u043E\u043B\u044F \u0432 \u043E\u0431\u0449\u0435\u0439 \u0442\u0435\u043E\u0440\u0438\u0438 \u043E\u0442\u043D\u043E\u0441\u0438\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u0438, \u0441\u0432\u044F\u0437\u044B\u0432\u0430\u044E\u0449\u0438\u0435 \u043C\u0435\u0436\u0434\u0443 \u0441\u043E\u0431\u043E\u0439 \u043C\u0435\u0442\u0440\u0438\u043A\u0443 \u0438\u0441\u043A\u0440\u0438\u0432\u043B\u0451\u043D\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0430-\u0432\u0440\u0435\u043C\u0435\u043D\u0438 \u0441\u043E \u0441\u0432\u043E\u0439\u0441\u0442\u0432\u0430\u043C\u0438 \u0437\u0430\u043F\u043E\u043B\u043D\u044F\u044E\u0449\u0435\u0439 \u0435\u0433\u043E \u043C\u0430\u0442\u0435\u0440\u0438\u0438. \u0422\u0435\u0440\u043C\u0438\u043D \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u0443\u0435\u0442\u0441\u044F \u0438 \u0432 \u0435\u0434\u0438\u043D\u0441\u0442\u0432\u0435\u043D\u043D\u043E\u043C \u0447\u0438\u0441\u043B\u0435: \u00AB\u0443\u0440\u0430\u0432\u043D\u0435\u0301\u043D\u0438\u0435 \u042D\u0439\u043D\u0448\u0442\u0435\u0301\u0439\u043D\u0430\u00BB, \u0442\u0430\u043A \u043A\u0430\u043A \u0432 \u0442\u0435\u043D\u0437\u043E\u0440\u043D\u043E\u0439 \u0437\u0430\u043F\u0438\u0441\u0438 \u044D\u0442\u043E \u043E\u0434\u043D\u043E \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0435, \u0445\u043E\u0442\u044F \u0432 \u043A\u043E\u043C\u043F\u043E\u043D\u0435\u043D\u0442\u0430\u0445 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u044F\u0435\u0442 \u0441\u043E\u0431\u043E\u0439 \u0441\u0438\u0441\u0442\u0435\u043C\u0443 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0439. \u0412\u044B\u0433\u043B\u044F\u0434\u044F\u0442 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F \u0441\u043B\u0435\u0434\u0443\u044E\u0449\u0438\u043C \u043E\u0431\u0440\u0430\u0437\u043E\u043C: <math>R_{ab} - {R \\over 2} g_{ab} + \\Lambda g_{ab} = {8 \\pi G \\over c^4} T_{ab}</math> \u0433\u0434\u0435 <math>R_{ab}</math> \u2014 \u0442\u0435\u043D\u0437\u043E\u0440 \u0420\u0438\u0447\u0447\u0438, \u043F\u043E\u043B\u0443\u0447\u0430\u044E\u0449\u0438\u0439\u0441\u044F \u0438\u0437 \u0442\u0435\u043D\u0437\u043E\u0440\u0430 \u043A\u0440\u0438\u0432\u0438\u0437\u043D\u044B \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0430-\u0432\u0440\u0435\u043C\u0435\u043D\u0438 <math>R_{abcd}</math> \u043F\u043E\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u043E\u043C \u0441\u0432\u0451\u0440\u0442\u043A\u0438 \u0435\u0433\u043E \u043F\u043E \u043F\u0430\u0440\u0435 \u0438\u043D\u0434\u0435\u043A\u0441\u043E\u0432, R \u2014 \u0441\u043A\u0430\u043B\u044F\u0440\u043D\u0430\u044F \u043A\u0440\u0438\u0432\u0438\u0437\u043D\u0430, \u0442\u043E \u0435\u0441\u0442\u044C \u0441\u0432\u0451\u0440\u043D\u0443\u0442\u044B\u0439 \u0442\u0435\u043D\u0437\u043E\u0440 \u0420\u0438\u0447\u0447\u0438, <math>g_{ab}</math> \u2014 \u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u0442\u0435\u043D\u0437\u043E\u0440, <math>\\Lambda</math> \u2014 \u043A\u043E\u0441\u043C\u043E\u043B\u043E\u0433\u0438\u0447\u0435\u0441\u043A\u0430\u044F \u043F\u043E\u0441\u0442\u043E\u044F\u043D\u043D\u0430\u044F, \u0430 <math>T_{ab}</math> \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u044F\u0435\u0442 \u0441\u043E\u0431\u043E\u0439 \u0442\u0435\u043D\u0437\u043E\u0440 \u044D\u043D\u0435\u0440\u0433\u0438\u0438-\u0438\u043C\u043F\u0443\u043B\u044C\u0441\u0430 \u043C\u0430\u0442\u0435\u0440\u0438\u0438, (<math>\\pi</math> \u2014 \u0447\u0438\u0441\u043B\u043E \u043F\u0438, c \u2014 \u0441\u043A\u043E\u0440\u043E\u0441\u0442\u044C \u0441\u0432\u0435\u0442\u0430 \u0432 \u0432\u0430\u043A\u0443\u0443\u043C\u0435, G \u2014 \u0433\u0440\u0430\u0432\u0438\u0442\u0430\u0446\u0438\u043E\u043D\u043D\u0430\u044F \u043F\u043E\u0441\u0442\u043E\u044F\u043D\u043D\u0430\u044F \u041D\u044C\u044E\u0442\u043E\u043D\u0430). \u0422\u0430\u043A \u043A\u0430\u043A \u0432\u0441\u0435 \u0432\u0445\u043E\u0434\u044F\u0449\u0438\u0435 \u0432 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F \u0442\u0435\u043D\u0437\u043E\u0440\u044B \u0441\u0438\u043C\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u044B, \u0442\u043E \u0432 \u0447\u0435\u0442\u044B\u0440\u0451\u0445\u043C\u0435\u0440\u043D\u043E\u043C \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0435-\u0432\u0440\u0435\u043C\u0435\u043D\u0438 \u044D\u0442\u0438 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F \u0440\u0430\u0432\u043D\u043E\u0441\u0438\u043B\u044C\u043D\u044B 4\u00B7(4+1)/2=10 \u0441\u043A\u0430\u043B\u044F\u0440\u043D\u044B\u043C \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F\u043C. \u041E\u0434\u043D\u0438\u043C \u0438\u0437 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0435\u043D\u043D\u044B\u0445 \u0441\u0432\u043E\u0439\u0441\u0442\u0432 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0439 \u042D\u0439\u043D\u0448\u0442\u0435\u0439\u043D\u0430 \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u0438\u0445 \u043D\u0435\u043B\u0438\u043D\u0435\u0439\u043D\u043E\u0441\u0442\u044C, \u043F\u0440\u0438\u0432\u043E\u0434\u044F\u0449\u0430\u044F \u043A \u043D\u0435\u0432\u043E\u0437\u043C\u043E\u0436\u043D\u043E\u0441\u0442\u0438 \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u043E\u0432\u0430\u043D\u0438\u044F \u043F\u0440\u0438 \u0438\u0445 \u0440\u0435\u0448\u0435\u043D\u0438\u0438 \u043F\u0440\u0438\u043D\u0446\u0438\u043F\u0430 \u0441\u0443\u043F\u0435\u0440\u043F\u043E\u0437\u0438\u0446\u0438\u0438."@ru ; rdfs:comment "Einsteins feltligninger (EFL) er et sett med ti ligninger, redusert fra seksten grunnet symmetri, i Einsteins generelle relativitetsteori som er en teori for gravitasjon. Denne teorien beskriver gravitasjon som en krumning av tidrommet som f\u00F8lge av masse og energi. EFL uttrykker proporsjonalitetsforholdet mellom disse egenskapene. Ligningene ble f\u00F8rst publisert i 1915."@no , "Relativitat general Fitxer:Neutronstar Light Deflection."@ca , "R\u00F3wnanie Einsteina to r\u00F3wnanie pola og\u00F3lnej teorii wzgl\u0119dno\u015Bci."@pl , ""@zh , ""@ja , "Em f\u00EDsica, a equa\u00E7\u00E3o de campo de Einstein ou a equa\u00E7\u00E3o Einstein \u00E9 uma equa\u00E7\u00E3o na teoria da gravita\u00E7\u00E3o, chamada relatividade geral, que descreve como a mat\u00E9ria gera gravidade e, inversamente, como a gravidade afeta a mat\u00E9ria. A equa\u00E7\u00E3o do campo de Einstein se reduz \u00E0 lei de Newton da gravidade no limite n\u00E3o-relativista, isto \u00E9, \u00E0 velocidades baixas e campos gravitacionais pouco intensos."@pt , "En f\u00EDsica, la ecuaci\u00F3n del campo de Einstein o la ecuaci\u00F3n de Einstein es una ecuaci\u00F3n en la teor\u00EDa de la gravitaci\u00F3n, llamada relatividad general, que describe c\u00F3mo la materia crea gravedad e, inversamente, c\u00F3mo la gravedad afecta la materia. La ecuaci\u00F3n del campo de Einstein se reduce a la ley de Newton de la gravedad en el l\u00EDmite no-relativista, esto es, a velocidades bajas y campos gravitacionales d\u00E9biles."@es , "Ecua\u0163iile lui Einstein, au fost descoperite de David Hilbert \u015Fi Albert Einstein practic concomitent \u00EEn anul 1915. Ele reprezint\u0103 un sistem de ecua\u0163ii diferen\u0163iale neliniare de gradul 2 din care fac parte tensorii metric, Ricci \u015Fi energie -impuls al sursei, scalarul Ricci. Tensorul Ricci de rang 2 se ob\u0163ine din tensorul antisimetric dup\u0103 perechile de indici de rang 4 Riemann, iar scalarul Ricci se ob\u0163ine de pe urma tensorului Ricci."@ro , "Einstein alan denklemleri ya da Einstein denklemleri (k\u0131saca EAD), y\u00FCksek h\u0131z ve b\u00FCy\u00FCk k\u00FCtlelerde ge\u00E7erli olan uzayzaman\u0131n geometrisi ile enerji ve momentum da\u011F\u0131l\u0131m\u0131n\u0131 ili\u015Fkilendiren do\u011Frusal olmayan diferansiyel denklemler k\u00FCmesidir. Einstein, bu denklemleri ilk kez 1915 y\u0131l\u0131nda yay\u0131mlam\u0131\u015Ft\u0131r. Bu denklemler, uzayzaman\u0131n e\u011Frili\u011Fini momentum ve enerji da\u011F\u0131l\u0131m\u0131na e\u015Fde\u011Ferlik ilkesi ile e\u015Fleyen on denklemden olu\u015Fur."@tr , "Einsteinin kentt\u00E4yht\u00E4l\u00F6t tai Einsteinin yht\u00E4l\u00F6t ovat kymmenen Albert Einsteinin yleisen suhteellisuusteorian yht\u00E4l\u00F6\u00E4, jotka kuvaavat gravitaation massan ja energian aiheuttamana aika-avaruuden kaareutumana. Tarkalleen ottaen kentt\u00E4yht\u00E4l\u00F6t ilmaisevat yhteyden avaruuden geometrian ja siell\u00E4 olevan massan ja energian v\u00E4lill\u00E4."@fi , "L'\u00E9quation d'Einstein ou \u00E9quation de champ d'Einstein est l'\u00E9quation aux d\u00E9riv\u00E9es partielles principale de la relativit\u00E9 g\u00E9n\u00E9rale. C'est une \u00E9quation dynamique qui d\u00E9crit comment la mati\u00E8re et l'\u00E9nergie modifient la g\u00E9om\u00E9trie de l'espace-temps. Cette courbure de la g\u00E9om\u00E9trie autour d'une source de mati\u00E8re est alors interpr\u00E9t\u00E9e comme le champ gravitationnel de cette source. Le mouvement des objets dans ce champ est d\u00E9crit tr\u00E8s pr\u00E9cis\u00E9ment par l'\u00E9quation de sa g\u00E9od\u00E9sique."@fr , "\u0420\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0415\u0439\u043D\u0448\u0442\u0435\u0439\u043D\u0430 - \u043E\u0441\u043D\u043E\u0432\u043D\u0456 \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0437\u0430\u0433\u0430\u043B\u044C\u043D\u043E\u0457 \u0442\u0435\u043E\u0440\u0456\u0457 \u0432\u0456\u0434\u043D\u043E\u0441\u043D\u043E\u0441\u0442\u0456."@uk , "The Einstein field equations (EFE) or Einstein's equations are a set of ten equations in Einstein's theory of general relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy. First published by Einstein in 1915 as a tensor equation, the EFE equate spacetime curvature (expressed by the Einstein tensor) with the energy and momentum within that spacetime (expressed by the stress-energy tensor)."@en , "L'equazione di campo di Einstein \u00E8 il risultato finale della teoria della relativit\u00E0 generale, sviluppata da Albert Einstein nel 1915. \u00C8 stata al centro di una polemica di priorit\u00E0 tra lo stesso Einstein ed il matematico David Hilbert, risolta solo recentemente a favore di Einstein. In breve, le equazioni di campo di Einstein descrivono la curvatura dello spaziotempo, in funzione della densit\u00E0 di materia, dell'energia e della pressione, rappresentate tramite il tensore stress-energia T."@it , "\u0423\u0440\u0430\u0432\u043D\u0435\u0301\u043D\u0438\u044F \u042D\u0439\u043D\u0448\u0442\u0435\u0301\u0439\u043D\u0430 (\u0438\u043D\u043E\u0433\u0434\u0430 \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u0435\u0442\u0441\u044F \u043D\u0430\u0437\u0432\u0430\u043D\u0438\u0435 \u00AB\u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F \u042D\u0439\u043D\u0448\u0442\u0435\u0439\u043D\u0430-\u0413\u0438\u043B\u044C\u0431\u0435\u0440\u0442\u0430\u00BB) \u2014 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F \u0433\u0440\u0430\u0432\u0438\u0442\u0430\u0446\u0438\u043E\u043D\u043D\u043E\u0433\u043E \u043F\u043E\u043B\u044F \u0432 \u043E\u0431\u0449\u0435\u0439 \u0442\u0435\u043E\u0440\u0438\u0438 \u043E\u0442\u043D\u043E\u0441\u0438\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u0438, \u0441\u0432\u044F\u0437\u044B\u0432\u0430\u044E\u0449\u0438\u0435 \u043C\u0435\u0436\u0434\u0443 \u0441\u043E\u0431\u043E\u0439 \u043C\u0435\u0442\u0440\u0438\u043A\u0443 \u0438\u0441\u043A\u0440\u0438\u0432\u043B\u0451\u043D\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0430-\u0432\u0440\u0435\u043C\u0435\u043D\u0438 \u0441\u043E \u0441\u0432\u043E\u0439\u0441\u0442\u0432\u0430\u043C\u0438 \u0437\u0430\u043F\u043E\u043B\u043D\u044F\u044E\u0449\u0435\u0439 \u0435\u0433\u043E \u043C\u0430\u0442\u0435\u0440\u0438\u0438."@ru , "De Einstein-vergelijkingen zijn een set van vergelijkingen die de algemene relativiteitstheorie van Einstein samenvatten. Net zoals Newton zijn zwaartekrachtstheorie zeer bondig en concreet samenvatte in essentieel \u00E9\u00E9n formule, de Gravitatiewet van Newton, zijn de Einstein-vergelijkingen een concrete wiskundige uitdrukking van Einsteins gehele relativiteitstheorie."@nl , "Im Rahmen der allgemeinen Relativit\u00E4tstheorie wird durch die einsteinschen Feldgleichungen, auch Einsteingleichungen, Einstein-Hilbert-Gleichungen oder Gravitationsgleichungen, das physikalische Ph\u00E4nomen der Gravitation klassisch beschrieben."@de . @prefix skos: . @prefix ns9: . dbpedia:Einstein_field_equations skos:subject ns9:General_relativity , ns9:Albert_Einstein , ns9:Partial_differential_equations . @prefix ns10: . dbpedia:Einstein_field_equations dbpprop:hasPhotoCollection ns10:Einstein_field_equations . @prefix dbpedia-owl: . dbpedia:Albert_Einstein dbpedia-owl:knownFor dbpedia:Einstein_field_equations . @prefix ns12: . dbpedia:Albert_Einstein ns12:knownFor dbpedia:Einstein_field_equations ; dbpprop:knownFor dbpedia:Einstein_field_equations . dbpprop:redirect dbpedia:Einstein_field_equations , dbpedia:Einstein_field_equations , dbpedia:Einstein_field_equations . dbpedia:Einstein_Field_Equations dbpprop:redirect dbpedia:Einstein_field_equations . dbpedia:Einstein_equation dbpprop:redirect dbpedia:Einstein_field_equations . dbpprop:redirect dbpedia:Einstein_field_equations . dbpedia:Mass-energy_tensor dbpprop:redirect dbpedia:Einstein_field_equations . dbpprop:redirect dbpedia:Einstein_field_equations , dbpedia:Einstein_field_equations . dbpedia:Einstein_equations dbpprop:redirect dbpedia:Einstein_field_equations . dbpedia:Einstein_field_equation dbpprop:redirect dbpedia:Einstein_field_equations . dbpedia:Vacuum_field_equations dbpprop:redirect dbpedia:Einstein_field_equations . @prefix yago: . yago:Einstein_field_equations owl:sameAs dbpedia:Einstein_field_equations .