{"title":"关于$5D$宇宙的$（1+1+3）$线程的爱因斯坦场方程的分裂","authors":"A. Bejancu, H. Farran","doi":"10.36890/IEJG.902162","DOIUrl":null,"url":null,"abstract":"We obtain a new and simple splitting of Einstein field equations with respect to the (1 + 1 + 3) threading of a 5 D universe ( ¯ M, ¯ g ) . The study is based on the spatial tensor fields and on the Riemannian spatial connection, which behave as 3 D geometric objects. All the equations are expressed with respect to the adapted frame field and the adapted coframe field induced by the (1 + 1 + 3) threading of ( ¯ M, ¯ g ) . In particular, we obtain the splitting of the Einstein field equations in a 5 D Robertson-Walker universe.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Splitting of the Einstein Field Equations with Respect to the $(1+1+3)$ Threading of a $5D$ Universe\",\"authors\":\"A. Bejancu, H. Farran\",\"doi\":\"10.36890/IEJG.902162\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We obtain a new and simple splitting of Einstein field equations with respect to the (1 + 1 + 3) threading of a 5 D universe ( ¯ M, ¯ g ) . The study is based on the spatial tensor fields and on the Riemannian spatial connection, which behave as 3 D geometric objects. All the equations are expressed with respect to the adapted frame field and the adapted coframe field induced by the (1 + 1 + 3) threading of ( ¯ M, ¯ g ) . In particular, we obtain the splitting of the Einstein field equations in a 5 D Robertson-Walker universe.\",\"PeriodicalId\":43768,\"journal\":{\"name\":\"International Electronic Journal of Geometry\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-03-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Electronic Journal of Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.36890/IEJG.902162\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Electronic Journal of Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.36890/IEJG.902162","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Splitting of the Einstein Field Equations with Respect to the $(1+1+3)$ Threading of a $5D$ Universe
We obtain a new and simple splitting of Einstein field equations with respect to the (1 + 1 + 3) threading of a 5 D universe ( ¯ M, ¯ g ) . The study is based on the spatial tensor fields and on the Riemannian spatial connection, which behave as 3 D geometric objects. All the equations are expressed with respect to the adapted frame field and the adapted coframe field induced by the (1 + 1 + 3) threading of ( ¯ M, ¯ g ) . In particular, we obtain the splitting of the Einstein field equations in a 5 D Robertson-Walker universe.
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