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Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 2

On generalized Robertson Walker spacetimes satisfying some curvature condition

Cengizhan MURATHAN
Kadri ARSLAN
Ryszard DESZCZ
Marian HOTLOS
Ridvan EZENTAS
Pages
353–373
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

They are quasi-Einstein, i.e. at every point of M rank (S − α g) ⩽ 1, for some α ∈ R, or non-quasi-Einstein.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We give necessary and sufficient conditions for warped product manifolds (M, g), of dimension ⩾ 4, with 1 -dimensional base, and in particular, for generalized Robertson–Walker spacetimes, to satisfy some generalized Einstein metric condition.
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Key Findings & Data:Namely, the difference tensor R·C−C ·R, formed from the curvature tensor R and the Weyl conformal curvature tensor C , is expressed by the Tachibana tensor Q(S, R) formed from the Ricci tensor S and R.
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Conclusion & Impact:They are quasi-Einstein, i.e. at every point of M rank (S − α g) ⩽ 1, for some α ∈ R, or non-quasi-Einstein.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

We give necessary and sufficient conditions for warped product manifolds (M, g), of dimension ⩾ 4, with 1 -dimensional base, and in particular, for generalized Robertson–Walker spacetimes, to satisfy some generalized Einstein metric condition. Namely, the difference tensor R·C−C ·R, formed from the curvature tensor R and the Weyl conformal curvature tensor C , is expressed by the Tachibana tensor Q(S, R) formed from the Ricci tensor S and R. We also construct suitable examples of such manifolds. They are quasi-Einstein, i.e. at every point of M rank (S − α g) ⩽ 1, for some α ∈ R, or non-quasi-Einstein.

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Cite This Article

MURATHAN, C., ARSLAN, K., DESZCZ, R., HOTLOS, M., EZENTAS, R. (2022). On generalized Robertson Walker spacetimes satisfying some curvature condition. Turkish Journal of Mathematics, Cilt: 38 - Sayı: 2, 353–373. https://ajindex.com/articles/608283

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