Thermodynamics of Einstein–Euler–Heisenberg black holes with thermal fluctuations and nonlinear electromagnetic fields

Abstract This work mainly focuses on the nonlinear Einstein–Euler–Heisenberg theory and its applications from various aspects. Firstly, thermodynamic variables are analytically determined via Smarr formula for a four-dimensional spherically symmetric Einstein–Euler–Heisenberg black hole by taking the Hawking–Bekenstein entropy as the basis. The results are supported by graphical illustrations for certain Euler–Heisenberg and electric charge parameters, which are in turn used for making further comments on the stability and possible critical points of the concerned black hole. The thermodynamic analyses are then repeated for two distinct cases in which entropy is subject to a logarithmic and an exponential correction, respectively. Our assessments have shown that statistical quantum fluctuations and nonlinear electrodynamic effects can alter the stability and the thermodynamic properties of black holes. Finally, the one-sided bending angle and the gravitational redshift of light are determined in the vicinity of astronomical structures obeying the nonlinear Einstein–Euler–Heisenberg model and the results obtained are applied to three electrically charged, compact stars.