On spacetimes with a semi-symmetric recurrent metric connection

In this paper, we deal with spacetimes allowing a semi-symmetric connection whose metric tensor is recurrent. We investigate the impact of this connection on spacetimes and establish a nontrivial example. We physically explain the properties of spacetime that we obtained. Under a certain condition, we demostrate that a spacetime admitting such a connection becomes the GRW spacetime as well as the anti-de Sitter and represents the dark matter era. Finally, we scrutinize in case such a spacetime admits a Ricci soliton and generalized Ricci soliton.