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本文研究了带有整体单极的Reissner-Nordstrom-AdS黑洞在扩展相空间中出射粒子的量子隧穿辐射过程. 其中, 将宇宙学参数视为动态变量而不同于之前研究工作中将其视为常数而忽略其贡献. 具体地, 在计算出射粒子隧穿率时将宇宙学参数引入计算并将其解释为热力学压强. 计算结果表明, 出射粒子的隧穿率与粒子出射前后黑洞的贝肯斯坦-霍金熵差成正比, 辐射谱偏离了纯热谱, 该结果与将宇宙学参数视为常数的情况完全相同. 这意味着在扩展相空间中可以得到粒子的隧穿概率, 并且隧穿过程不依赖于热力学状参量, 这一工作自然地进一步将霍金辐射推广到了带有整体单极Reissner-Nordstrom-AdS黑洞扩展相空间中. 结果表明, 整体单极子尽管影响粒子的动力学行为和热力学量, 但并不影响熵变和隧穿率.In recent years, thermodynamics and phase transitions of black holes in extended phase space have been extensively studied. The results show that the original first law of thermodynamics needs revising 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 work focuses on this topic, that is, to calculate the specific value of the tunneling probability in the extended phase space and ascertains whether the results obtained in the normal phase space are consistent with those in the extended phase space. The methods used herein are described below. Taking Reissner-Nordstrom-AdS black holes with global monopole for example, the cosmological parameters are regarded as dynamic variables, which is different from previous treatment methods that regard them as constants and ignore their contributions to the tunneling probability. In particular, cosmological parameters are introduced and regarded as thermodynamic pressure when the tunneling probability is calculated, and their contribution to the tunneling probability is considered. In the work the tunneling process of mass particles is mainly studied. The outgoing particles are viewed as spherical de Broglie waves, and then the relative phase velocity and group velocity are calculated. The geodesic equation is obtained according to the relationship between the two velocities, and the tunneling probability is calculated from the geodesic equation. It is concluded that the results show that the tunneling probability of the ingoing particles is proportional to the difference in 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 entropy change or 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.
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