Hawking radiation from a Reissner-Nordstrom-AdS black hole with integral monopoles in extended phase space

Abstract

In recent years, thermodynamics and phase transitions of black holes in extended phase Spaces have been extensively studied. The results show that the original first law of thermodynamics will be revised and new phase transitions will appear. However, so far, Hawking tunneling radiation has not been widely studied in the extended phase space. In particular, whether the tunneling radiation probability changes at this time is still uncertain. This paper intends to focus on this topic, that is, to calculate the specific value of the tunneling probability in the extended phase space and compare whether the results obtained in the normal phase space are consistent with that in the extended phase space. Methods:We takes the Reissner-Nordstrom-AdS black holes with global monopole as an example and treat the cosmological parameters as dynamic variables, unlike in the previous work where it is treatedas constants and its contributions to the tunneling probability are ignored. In particular, cosmological parameters are introduced and interpreted as thermodynamic pressure when the tunneling probabilityis calculated, and its contribution to the tunneling probability is considered. We mainly study the tunneling process of mass particles. The outgoing particles are viewed as spherical de Broglie waves, and then the phase velocity and group velocity relative to it are calculated. The geodesic equation is obtained according to the relationship between the two velocity, and the tunneling probability is calculated according to the geodesic equation. Conclusion:The results show that the tunneling probability of the ingoing particles is proportional to the difference of the Bekenstein-Hawking entropy of the black hole before and after the particles tunnel, and the radiation spectrum deviates from the pure thermal spectrum, which is exactly the same as the case that the cosmological parameters are treated as constants. This means that the tunneling probability of particles can be obtained in the extended phase space, and the tunneling process does not depend on thermodynamic parameters. In addition, it is found that although the global monopole affects the dynamical behavior and thermodynamic quantity of the particle, it does not affect the difference of the entropy and tunneling rate. In other words, the conclusion that the tunneling probability in extended phase space is exactly the same as that in normal phase space does not depend on the space-time topology.