Critical orbits in Schwarzschild black hole with quintessence and string cloud background space-times

In this paper, we have examined the geodesic structure of the spacetime surrounding Schwarzschild black holes in the presence of a quintessence field parameter q and string cloud parameter a. Because of the quintessence field, there are two horizon structures and coordinate time t shows some fascinating variations due to the parameters. We do a thorough investigation of the existence of critical orbits for various parameter values