Effect of quantum gravity on thermodynamical properties of Reissner–Nordström–NUT–Kiselev–Rastall black holes

In this paper, we study the effect of quantum gravity on the thermal property of the Reissner–Nordström–NUT–Kiselev–Rastall (RN-NUT-KR) black hole in the context of the tunneling process of scalar/fermion particles. We analyze the tunneling radiation by using the electromagnetic Klein–Gordon equation and the electromagnetic Dirac equation generalized with the modified fundamental commutation relations. We solve these equations by the Hamilton–Jacobi ansatz with the semiclassical WKB approximation. The modified Hawking temperature of the black hole depends not only on the black hole background but also on the emitted particle’s quantum numbers. The quintessence and Rastall parameters increase the Hawking temperature for small black holes, while the quantum gravity effect decelerates the temperature increasing in the evaporation process and causes the black holes to remain as remnants. We also compute the modified heat capacity and modified Gibbs free energy and investigate the thermodynamic stability conditions and phase transitions.