Abstract: A concircularly semi-symmetric metric connection is a special class of semi-symmetric metric connection when its generator is a concircular vector. In this talk, we will present results on this connection on pseudo-Riemannian manifolds, and in particular, we will observe the application to Lorentzian manifolds and the theory of relativity. We demonstrate that a Lorentzian manifold reduces to a GRW space-time when the generator of the observed connection is a unit timelike vector. At the same time, the mentioned connection becomes a semi-symmetric metric P-connection. At the end, we determine the equation of state on a perfect fluid space-time. These are the results of a joint work with prof. Milan Zlatanović published in J. Geom. Phys. 217 (2025).