Effective quantum gravity black hole with cloud of strings surrounded by quintessence field

In this study, we investigate a static, spherically symmetric black hole (BH) within the framework of Effective Quantum Gravity (EQG) in the presence of a cloud of strings (CS) and a quintessence field (QF). We derive the modified metric function incorporating quantum corrections and analyze its impact on the horizon structure, geodesic motion, shadow formation, scalar perturbations, and thermodynamics. The metric function is influenced by three key parameters: the quantum correction parameter xi, the CS parameter alpha, and the parameters (c, w) of the QF. Our results reveal that increasing xi primarily influences the Cauchy horizon, causing it to expand, while having a negligible effect on the event and cosmological horizons. On the other hand, larger values of alpha and c lead to an increase in the event horizon radius while reducing the cosmological horizon. The study of null and time-like geodesics indicates that quantum effects modify photon trajectories and the stability of circular orbits. We derive analytical expressions for the radius of the photon sphere and the BH shadow. Our findings indicate that the presence of QF and CS enlarges the shadow radius, whereas the incorporation of effective quantum corrections (xi) reduces it. Using the Regge-Wheeler equation, we analyze scalar perturbations and greybody factors, demonstrating that xi suppresses transmission probabilities while enhancing reflection coefficients. This study paves the way for further exploration of EQG-modified rotating BHs, gravitational wave emissions, and astrophysical tests of quantum corrections in future observational studies.