Effects of Non-linear Electrodynamics on Thermodynamics of Charged Black Hole

This paper investigates thermodynamics, quasi-normal modes, thermal fluctuations and phase transitions of Reissner-Nordstr\"om black hole with the effects of non-linear electrodynamics. We first compute the expressions for Hawking temperature, entropy and heat capacity of this black hole and then obtain a relation between Davies's point and quasi-normal modes with non-linear electrodynamics. We also observe the effects of logarithmic corrections on uncorrected thermodynamic quantities such as entropy, Hawking temperature, Helmholtz free energy, internal energy, Gibbs free energy, enthalpy and heat capacity. It is found that presence of non-linear electrodynamic parameter induces more instability in black holes of large radii. Finally, we analyze the phase transitions of Hawking temperature as well as heat capacity in terms of entropy for different values of charge ($q$), horizon radius ($r_{+}$) and coupling parameter ($\alpha$). We obtain that Hawking temperature changes its phase from positive to negative for increasing values of $q$ and $r_{+}$ while it shows opposite trend for higher values of $\alpha$. The heat capacity changes its phase from negative to positive for large values of charge, horizon radius and coupling parameter.