Thermal fluctuations, quasi-normal modes and phase transition of the charged AdS black hole with perfect fluid dark matter

In this paper, we study thermodynamics, thermal fluctuations, phase transitions and the charged anti-de Sitter black hole surrounded by perfect fluid dark matter. Large black holes are shown to be stable when subject to thermal fluctuations, and we begin by exploring how these fluctuations affect the uncorrected thermodynamic quantities of entropy, Helmholtz free energy, Gibbs free energy, enthalpy specific heat, and phase transition stability. We also discuss null geodesics and the radius of the photon sphere for the charged AdS BH and use the radius of a photon sphere to calculate the Lyapunov exponent and angular velocity. Exceptionally, we test the effects of various parameters of a black hole graphically by observing the existence of the correction parameter and the coupling parameter, which reveal the behavior of corrected thermodynamic quantities. Lastly, we see how the system is stable (under the effects of the dark matter parameter) by figuring out the specific heat and Hawking temperature, which are both related to entropy.

Automated summary

In this paper, we investigate the stability of large black holes under thermal fluctuations and explore the effects of these fluctuations on thermodynamic quantities and phase transition stability. We also examine null geodesics and photon sphere radius for a charged AdS BH and calculate the Lyapunov exponent and angular velocity. Additionally, we test the behavior of corrected thermodynamic quantities by observing the effects of correction and coupling parameters. Finally, we determine the stability of the system (under the influence of dark matter) by analyzing the specific heat and Hawking temperature, both of which are related to entropy.