Quantum gravity correction to the thermodynamic quantities of the charged dRGT black hole

In this study, in the framework of the Hamilton approach, the quantum gravity effect on Hawking temperature, on the specific heat capacity, and on the stability conditions of the charged de Rham, Gabadadze, and Tolley (dRGT) black hole are investigated by using the tunneling processes of both charged massive scalar and Dirac particles. It is shown that quantum corrected Hawking temperature depends not only on the black hole properties but also on the properties of the tunnelling particles. It is also observed that quantum corrected Hawking temperature is lower than that of the standard Hawking temperature. Also, the specific heat capacity and the local stability conditions of the black hole are discussed in the context of the tunneling processes of both charged massive scalar and Dirac particles in the presence of quantum gravity effect. It is observed that the black hole might undergo second-type phase transitions to become stable during the tunneling processes of both scalar and Dirac particles. However, in the absence of the quantum gravity effect, the black hole might undergo the both first-type and second-type phase transitions to become stable.