Geometric and Thermodynamic Properties of Frolov Black Holes with Topological Defects

We investigated a modified Frolov black hole (BH) model that incorporates both a global monopole (GM) and a cosmic string (CS) to explore the interplay between non-singular BH regularization and topological defect effects. In our study, we derived a spacetime metric characterized by a regulated core through a length scale parameter $α$ and introduced additional modifications via the GM parameter $η$ and the CS parameter $a$, which collectively alter the horizon structure and causal geometry of the BH. We analyzed the thermodynamic properties by deriving expressions for the mass function, Hawking temperature, and entropy, and found that the inclusion of GM and CS significantly deviates the BH entropy from the conventional Bekenstein-Hawking area law, while numerical investigations showed that the shadow radius exhibits contrasting behaviors: the Frolov parameters tend to reduce the shadow size whereas the topological defects enhance it. Furthermore, we examined the dynamics of scalar and electromagnetic perturbations by solving the massless Klein-Gordon equation in the BH background and computed the quasinormal modes (QNMs) using the WKB approximation, which confirmed the BH's stability and revealed that the oscillation frequencies and damping rates are strongly dependent on the parameters $α$, $q$, $η$, and $a$. Our results suggest that the distinct observational signatures arising from this composite BH model may provide a promising avenue for testing modified gravity theories in the strong-field regime.