Observational properties and quasinormal Modes of the Hayward black Hole surrounded by a cloud of strings

Abstract

In this work, we explored the Hayward black hole surrounded by a cloud of strings, with a focus on the effects of the regularization parameter $l$ and the string cloud parameter $a$ on its observational properties and quasinormal modes (QNMs). Utilizing the spacetime metric and geodesic equations, we calculated several geometric quantities characterizing the black hole. To visualize the observational appearance of the accretion disk, we employed the Novikov--Thorne model to simulate both its primary and secondary images. Furthermore, we analyzed the QNMs of the black hole under scalar and electromagnetic perturbations for different parameter values. The results indicate that as the regularization parameter $l$ increases, the outer horizon radius $r_{+}$, photon-sphere radius $r_{\text{ph}}$, critical impact parameter $b_{c}$, and innermost stable circular orbit $r_{\text{isco}}$ exhibit a gradual decrease, while the inner horizon radius $r_{-}$ and the real part of the QNMs frequency $\omega_{r}$ increase. In contrast, as the string cloud parameter $a$ increases, $r_{+}$, $r_{\text{ph}}$, $b_{c}$, and $r_{\text{ isco}}$ demonstrate a rapid increase, whereas $r_{-}$ and $\omega_{r}$ decrease. In both cases, the absolute value of the imaginary part of the QNMs frequency decreases with the increase $l$ or $a$. This work offers a theoretical foundation for understanding the coupling between regular black holes and surrounding string clouds.