Splitting of the Einstein Field Equations with Respect to the $(1+1+3)$ Threading of a $5D$ Universe

Authors : Aurel BEJANCU, Hani Reda FARRAN

Pages : 66-84

Doi:10.36890/iejg.902162

View : 68 | Download : 14

Publication Date : 2021-04-15

Article Type : Research Paper

Abstract :We obtain a new and simple splitting of Einstein field equations with respect to the $insert ignore into journalissuearticles values(1+1+3);$ threading of a $5D$ universe $insert ignore into journalissuearticles values(\bar{M}, \bar{g});$. The study is based on the spatial tensor fields and on the Riemannian spatial connection, which behave as $3D$ geometric objects. All the equations are expressed with respect to the adapted frame field and the adapted coframe field induced by the $insert ignore into journalissuearticles values(1+1+3);$ threading of $insert ignore into journalissuearticles values(\bar{M}, \bar{g});$. In particular, we obtain the splitting of the Einstein field equations in a $5D$ Robertson-Walker universe.
Keywords : Einstein field equations, spatial tensor fields, 3D geometric objects, 5D Robertson Walker universe

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