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

Abstract

We obtain a new and simple splitting of Einstein field equations with respect to the (1 + 1 + 3)threading of a 5D universe ( M; g). The study is based on the spatial tensor fields and on theRiemannian spatial connection, which behave as 3D geometric objects. All the equations areexpressed 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 equationsin a 5D Robertson-Walker universe.