Hawking Tunneling Radiation from the Gauss-Bonnet AdS Black Hole with Thermodynamic Pressure

By viewing the cosmological parameter Λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda $$\end{document} as a dynamic variable, the thermodynamics of AdS black holes has been successfully extended to the case with inclusion of the thermodynamic pressure P. In this thermodynamic state space, although one has presented many interesting physical phenomenons, the Hawking radiation with thermodynamic pressure and volume remains to unknown. In this paper, we investigate the Hawking radiation as a tunneling process from the five-dimensional neutral Gauss-Bonnet AdS black holes, where the cosmological parameter and the Gauss-Bonnet coupling parameter are not constant but viewed as dynamical variable quantities of the black holes. The results show that the tunnelling rate of emitted particles is proportional to the ratio of the initial entropy and final entropy of black hole. The exact emission spectrum thus deviates from the pure thermal spectrum, which is the same as the case that the cosmological parameter is constant. This means that the tunneling rate of particles can be obtained in the extended phase space and the tunneling process does not depend on the thermodynamic state space. Thus naturally extending the Hawking radiation framework to the extended phase space, and it’s consistent with an underlying unitary theory in the extended phase space.