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A new class of almost Ricci solitons and their physical interpretation. (English) Zbl 1428.83010
Summary: We establish a link between a connection symmetry, called conformal collineation, and almost Ricci soliton (in particular Ricci soliton) in reducible Ricci symmetric semi-Riemannian manifolds. As a physical application, by investigating the kinematic and dynamic properties of almost Ricci soliton manifolds, we present a physical model of imperfect fluid spacetimes. This model gives a general relation between the physical quantities $$(u, \mu, p, \alpha, \eta, \sigma_{i j})$$ of the matter tensor of the field equations and does not provide any exact solution. Therefore, we propose further study on finding exact solutions of our viscous fluid physical model for which it is required that the fluid velocity vector $$u$$ be tilted. We also suggest two open problems.
MSC:
 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) 35C08 Soliton solutions 53E20 Ricci flows
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References:
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