GRADIENT $\rho$-EINSTEIN SOLITONS AND APPLICATIONS
Abstract
In this paper, we mainly study gradient $\rho$-Einstein solitons on doubly warped product manifolds. More explicitly, we obtain necessary and sufficient conditions for a doubly warped product manifold to be a gradient $\rho$-Einstein soliton. We also apply our main result to warped product spacetime models such as generalized Robertson-Walker and standard static spacetimes as well as 3-dimensional Walker manifolds. We finally establish that there is no 3-dimensional essentially conformally symmetric gradient $\rho$-Einstein soliton.
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DOI: https://doi.org/10.22190/FUMI240813018G
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