  In this article, we characterize a Lorentzian manifold $\mathcal{M}$ with a
semi-symmetric metric connection. At first, we consider a semi-symmetric metric
connection whose curvature tensor vanishes and establish that if the associated
vector field is a unit time-like torse-forming vector field, then $\mathcal{M}$
becomes a perfect fluid spacetime. Moreover, we prove that if $\mathcal{M}$
admits a semi-symmetric metric connection whose Ricci tensor is symmetric and
torsion tensor is recurrent, then $\mathcal{M}$ represents a generalized
Robertson-Walker spacetime. Also, we show that if the associated vector field
of a semi-symmetric metric connection whose curvature tensor vanishes is a $f-$
Ric vector field, then the manifold is Einstein and if the associated vector
field is a torqued vector field, then the manifold becomes a perfect fluid
spacetime. Finally, we apply this connection to investigate Ricci solitons.
