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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In particular, we obtain the splitting of the Einstein field equations in a $5D$ Robertson-Walker universe.
📌 3 Key Takeaways
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Objective & Hypothesis:We obtain a new and simple splitting of Einstein field equations with respect to the $(1+1+3)$ threading of a $5D$ universe $(\bar{M}, \bar{g})$.
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Key Findings & Data:The study is based on the spatial tensor fields and on the Riemannian spatial connection, which behave as $3D$ geometric objects.
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Conclusion & Impact:In particular, we obtain the splitting of the Einstein field equations in a $5D$ Robertson-Walker universe.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Einstein field equations · spatial tensor fields · 3D geometric objects
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.
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Cite This Article
Bejancu, A., Farran, H. R. (2021). Splitting of the Einstein Field Equations with Respect to the $(1+1+3)$ Threading of a $5D$ Universe. International Electronic Journal of Geometry, Volume: 14 Issue: 1. https://doi.org/10.36890/iejg.902162