Generalized Robertson-Walker spacetimes extend the notion of Robertson-Walker spacetimes, by allowing for spatial non-homogeneity. A survey is presented, with main focus on Chen's characterization in terms of a timelike concircular vector. Together with their most important properties, some new results are presented.

Generalized Robertson-Walker space times, a survey

In this paper, it is proved that the fiber manifold M2 of a warped product manifold M = M1 ×fM2 inherits the Einstein-like class type of M whereas the base manifold does under some conditions. Some related results are considered.

Einstein-like warped product manifolds

This study aims mainly at investigating the effects of concircular flatness and concircular symmetry of a warped product manifold on its fibre and base manifolds. Concircularly flat and concircularly symmetric warped product manifolds are investigated. The divergence free concircular curvature tensor on warped product manifolds is considered. Finally, we apply some of these results to generalized Robertson-Walker and standard static space-times.

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Concircular curvature on warped product manifolds and applications.

Symmetries of f−associated standard static spacetimes and applications

Warped Product Manifolds

The purpose of the present article is to study and characterize several types of symmetries of generalized Robertson-Walker spacetimes. Conformal vector fields, curvature and Ricci collineations are studied. Many implications for existence of these symmetries on generalized Robertson-Walker spacetimes are obtained. Finally, Ricci solitons on generalized Robertson-Walker spacetimes admitting conformal vector fields are investigated.

On symmetries of generalized Robertson-Walker spacetimes and applications

The purpose of the present article is to study and characterize sev- eral types of symmetries of generalized Robertson-Walker space-times. Con- formal vector fields, curvature and Ricci collineations are studied. Many im- plications for existence of these symmetries on generalied Robertson-Walker spacetimes are obtained. Finally, Ricci solitons on generalized Robertson- Walker space-times admitting conformal vector fields are investigated.

On symmetries of generalized Robertson-Walker Space-times and applications

This article aimed to study and explore conformal vector fields on doubly warped product manifolds as well as on doubly warped spacetime. Then we derive sufficient conditions for matter and Ricci collineations on doubly warped product manifolds. A special attention is paid to concurrent vector fields. Finally, Ricci solitons on doubly warped product spacetime admitting conformal vector fields are considered.

/pdf/conformal-vector-fields-on-doubly-warped-product-manifolds-3c3ekmv62t.pdf

Conformal Vector Fields on Doubly Warped Product Manifolds and Applications

In this note, we study and explore locally symmetric f−associated standard static spacetimes If×M. Necessary and sufficient conditions on f−associated standard static spacetimes to be locally symmetric are derived. Some implications for these conditions are considered.

Noha Syied

Papers

On symmetries of generalized Robertson-Walker spacetimes and applications

On symmetries of generalized Robertson-Walker Space-times and applications

Conformal Vector Fields on Doubly Warped Product Manifolds and Applications

Symmetries of f−associated standard static spacetimes and applications

Locally symmetric f−associated standard static spacetimes