Ricci Semi-Symmetric Bulk Viscous String Fluid Spacetime in F(R,T)-Gravity and Energy Constraints for Penrose Theorem

This study is dedicated to a separable F(R,T)-gravity related to the bulk viscous string fluid to extract the equation of state for F(R,T)-gravity. In this research, we offer an insight into calculating the density and pressure in terms of string tension in the phantom barrier, stiff fluid, and matter-dominated eras. As demonstrated, if a spacetime in F(R,T)-gravity is full of bulk viscous string fluid matter, it is a generalized quasi-Einstein spacetime. In addition, we determine the equation of state of Ricci semi-symmetric and Ricci pseudo-symmetric spacetime in F(R,T)-gravity filled with bulk viscous string fluid matter. Finally, we try to give the energy constraints in view of Penrose’s singularity theorem of black holes for the spacetime in F(R,T)-gravity attached to bulk viscous string fluid.