Quantum first-order corrections of thermodynamic properties in a nonlinear electrodynamic black hole

In quantum electrodynamics, vacuum polarization leads to a nonlinear interaction between the electromagnetic fields. This interaction may give rise to nonlinear electrodynamics, which could significantly affect the nature of black holes. The asymptotically flat black hole solution in Einstein-nonlinear electrodynamics fields is examined. We investigate the nonlinear electrodynamic implications of black hole thermodynamics within the framework of the generalized uncertainty principle. Using the generalized uncertainty principle, the relativistic field equation was modified to solve the relativistic field equations of the nonlinear electrodynamic black hole at the outer horizon or inner horizon. To verify the generalized uncertainty principle’s influence on nonlinear electrodynamic black hole stability conditions and describe the tunneling radiation of nonlinear electrodynamic black holes affected by quantum gravity. Furthermore, we investigate the entropy and emission energy properties of the generalized uncertainty principle model, as well as its associated Hawking temperature. The logarithmic correction terms for entropy around the equilibrium state also assess the validity of the Hawking temperature of the first and third laws of thermodynamics in the presence of this correction term. In particular, we focus on the plasma falling radially from infinity to a black hole. Observers far away from a black hole see the size of the shadow due to the plasma. This discusses the possibility of the effect of plasma on the emission energy of supermassive black holes.