Quasi-normal modes, Emission rate and Shadow of the charged AdS black hole with perfect fluid dark matter

In this work we investigate a comprehensive examination of a charged AdS black hole surrounded by a distinct form of dark matter, focusing on key elements including the Hawking temperature, quasi-normal modes, emission rate, and the shadow. Our investigation commences by computing the Hawking temperature, thereby identifying critical values such as the black hole's critical radius and maximum temperature, essential in delineating its phase transition. Further exploration centers on the analysis of quasi-normal modes in charged AdS black holes immersed in perfect fluid dark matter (PFDM) within the massless scalar field paradigm. Employing the Wentzel-Kramers-Brillouin (WKB) method, we accurately derive the frequencies of these black hole quasi-normal modes (QNMs). Additionally, we conduct a meticulous assessment of how the intensity of the PFDM parameter $\alpha$ influences the partial absorption cross sections of the black hole, along with a detailed study of the energy emission rate's frequency variation. The pivotal role of geodesics in understanding astrophysical black hole characteristics is highlighted. Specifically, our investigation examines the influence of the dark matter parameter on photon evolution by computing the black hole's shadow radius. Our findings distinctly demonstrate the significant impact of the PFDM parameter $\alpha$ on the boundaries of the black hole's shadow, unveiling crucial insights into its features and interactions. This comprehensive analysis provides profound insights into the intricate dynamics between a charged AdS black hole, novel dark matter, and various physical phenomena, illuminating their interplay and contributing valuable knowledge to the understanding of these cosmic entities.