Probing the parameters of a Schwarzschild black hole surrounded by quintessence and cloud of strings through four standard astrophysical tests

In this paper, we concern about applying general relativistic tests on the spacetime produced by a static black hole associated with cloud of strings, in a universe filled with quintessence. The four tests we apply are precession of the perihelion in the planetary orbits, gravitational redshift, deflection of light, and the Shapiro time delay. Through this process, we constrain the spacetime’s parameters in the context of the observational data, which results in about $$\sim 10^{-9}$$ for the cloud of strings parameter, and $$\sim 10^{-20}$$ m$$^{-1}$$ for that of quintessence. The response of the black hole to the gravitational perturbations is also discussed