Quantum gravity effect on the Hawking radiation of charged rotating BTZ black hole

In this study, the quantum gravity effect on the tunnelling radiation of charged massive spin-0 scalar particle from 2+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2+1$$\end{document} dimensional charged rotating Banados–Teitelboim–Zanelli (BTZ) black hole is looked into by using the Hamilton–Jacobi approach. For this, we calculate the modified Hawking temperature of the black hole by using the modified Klein–Gordon equation based on the generalized uncertainty principle, and we noticed that the modified Hawking temperature of the black hole depends not only on the black hole properties, but also on the angular momentum, energy, charge and mass of the tunnelling scalar particle. Using the modified Hawking temperature, we discussed the stability of the black hole in the context of the modified heat capacity, and observed that it might undergo both first and 1 phase transitions in the presence of the quantum gravity effect, but just a first-type transition in the absence of the quantum gravity effect. Furthermore, we investigated the modified Hawking temperature of the black hole by using the tunnelling processes of the charged massive Dirac and vector boson particles. We observed that scalar, Dirac and vector particles are tunnelled from the black hole completely differently from each other in the presence of the quantum gravity effect.