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

Year 2021, Volume: 14 Issue: 1, 66 - 84, 15.04.2021

Aurel Bejancu Hani Reda Farran

https://doi.org/10.36890/iejg.902162

Abstract

We obtain a new and simple splitting of Einstein field equations with respect to the $(1+1+3)$ threading of a $5D$ universe $(\bar{M}, \bar{g})$. 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 $(1+1+3)$ threading of $(\bar{M}, \bar{g})$. 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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