Thermal fluctuations, quasi-normal modes and phase transitions of regular black hole

Abstract

In this paper, we study thermal fluctuations, quasi-normal modes and phase transitions of two black holes, i.e., regular Bardeen and Bardeen black hole surrounded by perfect fluid dark matter. We investigate the effects of thermal fluctuations on uncorrected thermodynamic quantities such as entropy, Hawking temperature, Helmholtz free energy, Gibbs free energy and thermal stability. It is found that large black holes are stable under the effect of thermal fluctuations. We then obtain a relation between Davies point and quasi-normal modes of a black hole with perfect fluid dark matter. Finally, we study the influence of magnetic charge, correction parameter and perfect fluid dark matter parameter (α) on Hawking temperature as well as heat capacity. It is found that phase transitions occur in Hawking temperature from positive to negative by increasing charge but it shows opposite behavior for higher values of α. The heat capacity changes its phase from positive to negative for large values of both magnetic charge as well as α.