Resumen:
By implementing the concept of polytropic structures as a scalar field gas with a dark energy-like behavior, we obtain a static spherically symmetric black hole solution in the framework of general relativity. In this paper, we study the quasinormal modes, the greybody bound process, the shadow behaviors, and the sparsity of black holes with a surrounding polytropic scalar field gas. Using the Wentzel-Kramers-Brillouin (WKB) approach, we evaluate the impact of a particular set of polytropic parameters (xi, A) with a fixed setting of the polytropic index n on the oscillation frequency and damping rate of gravitational waves. The results show that the effect of the parameter xi is much less significant than that of the parameter A on the gravitational waves oscillation frequency and damping rate. Furthermore, the analysis of the greybody factor bounds reveals special insight into the effect of certain parameters where the multipole moments l and the polytropic index n have similar effects, in contrast to the pair of polytropic parameters (xi, A). In light of such a comparative study, we investigate, on the other hand, the third-order Pade WKB method, which results in a more accurate process for quasinormal mode frequencies compared to the third-order standard WKB method. In this way, exploring the sparsity of Hawking radiation is another task that provides a better understanding of the behavior of the black hole solution. In this respect, the results show that the black hole behaves like blackbody radiation for a sufficiently large entropy. And for xi = A = 0, the relevant sparsity acts exactly like the Schwarzschild sparsity. These results provide an insight into the dynamics of black holes with a surrounding polytropic scalar field gas from the analysis of their quasinormal modes, greybody factors, shadow behaviors, energy emission rate and sparsity process. Constraints on the associated BH parameters, derived from the Event Horizon Telescope observations of M87" and Sgr A", indicate that this black hole model stands as a compelling candidate for representing astrophysical black holes.
