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 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.