On generalized Robertson-Walker spacetimes satisfying some curvature condition
Kadri Arslan, Ryszard Deszcz, Ridvan Ezentas, Marian Hotlo\'s and, Cengizhan Murathan
TL;DR
This paper establishes necessary and sufficient conditions for generalized Robertson-Walker spacetimes to satisfy certain generalized Einstein metric conditions, providing examples and exploring their quasi-Einstein properties.
Contribution
It offers a comprehensive characterization of warped product manifolds and generalized Robertson-Walker spacetimes under specific curvature conditions, including explicit examples.
Findings
Characterization of conditions for generalized Robertson-Walker spacetimes to satisfy generalized Einstein metrics
Construction of examples of such manifolds, including quasi-Einstein cases
Identification of conditions under which these manifolds are or are not quasi-Einstein
Abstract
We give necessary and sufficient conditions for warped product manifolds with 1-dimensional base, and in particular, for generalized Robertson-Walker spacetimes, to satisfy some generalized Einstein metric condition. We also construct suitable examples of such manifolds. They are quasi-Einstein or not.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds