Gradient $\rho$-Einstein Solitons and Applications

TL;DR

This paper investigates gradient $ ho$-Einstein solitons on doubly warped product manifolds, deriving conditions for their existence and applying results to various spacetime models, including Robertson-Walker and Walker manifolds.

Contribution

It provides necessary and sufficient conditions for gradient $ ho$-Einstein solitons on doubly warped products and explores their applications in spacetime geometries.

Findings

No 3-dimensional essentially conformally symmetric gradient $ ho$-Einstein solitons exist.

Conditions for gradient $ ho$-Einstein solitons are established for doubly warped products.

Applications to generalized Robertson-Walker and static spacetimes are demonstrated.

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 esentially conformally symmetric gradient $\rho$-Einstein soliton.