Abstract. The present discourse is based on the geometrical bearing of dust fluid and viscous fluid spacetime in terms of Ricci ρ-soliton and η-Ricci ρ-soliton in viscous fluid and dust fluid spacetime with torse-forming vector field ξ. A condition for the Ricci ρ-soliton to be steady, expanding or shrinking is also given. In particular case when the potential vector filed ξ of the soliton is of gradient type, we derive, from the η-Ricci ρ-soliton equation, a Laplacian equation.

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