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

Year 2021, , 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

References

• [1] Bejancu, A.:Kinematic quantities and Raychaudhuri equations in a 5D universe. The European Physical Journal C. 75 (7), 346 (2015).
• [2] Bejancu, A.:Equations of motion with respect to the (1 + 1 + 3) threading of a 5 D universe. The European Physical Journal C. 76 (1), 2 (2016).
• [3] Langlois, D.: Brane cosmology. Progress of Theoretical Physics Supplement. 148, 181–212 (2002).
• [4] Maartens, R., Kazuya K.: Brane-world gravity. Living Reviews in Relativity. 13 (1), 5 (2010).
• [5] Overduin, J.M., Wesson, P.S.: Kaluza-klein gravity. Physics Reports. 283 (5–6), 303–378 (1997).
• [6] Wesson, P.S.: Space-Time-Matter: Modern Kaluza-Klein Theory. World Sicentific. Singapore (1999).