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Solitons and gradient solitons on perfect fluid spacetime in \(f(\mathcal{R},T)\)-gravity. (English) Zbl 1498.53025

Summary: This research article attempts to examine the attribute of perfect fluid spacetime in \(f(\mathcal{R},T)\) gravity with a Killing velocity vector field \(\rho\) in terms of Ricci soliton, gradient Ricci soliton, Yamabe soliton, and gradient Yamabe soliton. Besides this, we evaluate a specific situation when the potential vector field \(\rho\) is of the form of gradient, we extract a modified Poisson equation, and modified Liouville equation from the Ricci soliton equation in \(f(\mathcal{R},T)\)-gravity stuffing with perfect fluids. In addition, we explore some harmonic significance of Ricci soliton on perfect fluid spacetime in \(f(\mathcal{R},T)\) gravity with a harmonic potential function \(\Psi \).

MSC:

53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53B50 Applications of local differential geometry to the sciences
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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