Analysis of Hawking Evaporation and Thermal Fluctuations of 4D Dyonic AdS Black Hole

Abstract

In the present thesis, we investigate the thermodynamic properties of dyonic AdS black hole (BH) along with the cosmological radius l, which is associated with the cosmolog- ical constant Λ. We investigate the BH horizon temperature T , which shows an increas- ing behaviour for different values of model parameters. We numerically solve the Stefan- Boltzmann equation and discuss the process of Hawking evaporation for the BH lifetime. The results indicate that with the emission of radiation, the overall mass of the BH expo- nentially decreases with the aid of the lifetime. We observe that the corrected entropy of AdS BH shows a positive increasing behaviour throughout the region of the BH event hori- zon. From the perspective of the stability of BHs, we observed that the physical behaviour of Helmholtz free energy, which shows a phase transition in the case of smaller BHs. We also discuss the stability of considering BH with the help of internal energy as well as heat capacity. In both cases, we notice that our constructed BH solutions show a first-order phase transition throughout the region of the BH space-time. The circular orbits of BH thermal profiles indicates that there exist a phase-transition, which is related with the BH horizon temperature. Finally, we concluded that our obtained results provide some deep insights into the BH thermodynamics and differentiate the present analysis from previous studies.