Abstract
In the present paper, we investigate the nature of Ricci-Yamabe soliton on an imperfect fluid generalized Robertson-Walker spacetime with a torse-forming vector fieldξ. Furthermore, if the potential vector fieldξof the Ricci-Yamabe soliton is of the gradient type, the Laplace-Poisson equation is derived. Also, we explore the harmonic aspects ofη-Ricci-Yamabe soliton on an imperfect fluidGRWspacetime with a harmonic potential functionψ. Finally, we examine necessary and sufficient conditions for a1-formη, which is theg-dual of the vector fieldξon imperfect fluidGRWspacetime to be a solution of the Schrödinger-Ricci equation.
Highlights
Symmetry is a beautiful property of the universe
Einstein equations which explain spacetime curvature evolution lead to current particle physics, equations in nuclear physics [1], astrophysics [2], and plasma physics [3]
In GR, the matter content of the universe is considered to work like an imperfect fluid in the standard cosmological models such as a time oriented 4-dimensional Lorentzian manifold
Summary
Symmetry is a beautiful property of the universe It is one of the fundamental concepts that can describe the laws of nature such as from general relativity to other physical theories. To understand the general theory of relativity, we study the model of relativistic fluids from the view of differential geometry. In [9], Ali and Ahsan studied the symmetries of space time manifold via Ricci solitons. Venkatesha and Aruna [11] used Ricci solitons in the study of perfect fluid spacetime admitting the potential vector field. We concentrate on the geometry of an imperfect fluid spacetime admitting the Ricci-Yamabe soliton and an eta-Ricci-Yamabe soliton to continue the work initiated in the past studies. We develop a new notion of RicciYamabe soliton and its extension η-Ricci-Yamabe soliton with the help of Ricci-Yamabe maps studied by Güler and Crasmareanu [15]
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