Abstract
In this paper, we studied the geometrical aspects of a perfect fluid spacetime in terms of conformal Ricci soliton and conformal [Formula: see text]-Ricci soliton with torse-forming vector field [Formula: see text]. Condition for the conformal Ricci soliton to be steady, expanding or shrinking are also given. In particular case, when the potential vector filed [Formula: see text] of the soliton is of gradient type, we derive, from the conformal [Formula: see text]-Ricci soliton equation, a Laplacian equation.