Recent work that treats the Hawking radiation as a semi-classical tunnelling process from the four-dimensional Schwarzschild and Reissner-Nordstrom black holes is extended to the case of higher dimensional Reissner-Nordstrom-de Sitter black holes. The result shows that the tunnelling rate is related to the change of Bekenstein-Hawking entropy and the exact radiant spectrum is no longer precisely thermal after considering the black hole background as dynamical and incorporating the self-gravitation effect of the emitted particles when the energy conservation and electric charge conservation are taken into account.

In consideration of the thermodynamic pressure and volume, we present a short and direct derivation of Hawking radiation as a tunneling process for the charged particles. Using Parikh's Semi-classical tunneling method and Lagrangian analysis on the action, we provide the geodesic equation of the massive particles via tunneling from the Anit-de Sitter (AdS) black hole. Special attention is given to calculating the imaginary part before and after particles via the horizon as the pressure and volume are considered. The result shows that the emission rates are always related to the change of Bekenstein-Hawking entropy and the exact spectrum is not precisely thermal, which are consistent with the case without pressure and volume.

In this paper, when considering the conservation of energy, electric charge and angular momentum, we develop the Parikh-Wilczek’s quantum tunneling method to study the Hawking radiation of charged particles via tunneling from the event horizon of Kim black hole. The result shows the exact radiation spectrum deviates from the precisely thermal one, but satisfies an underlying unitary theory, which provides a possible solution to the information loss during the black hole evaporation.

We investigate the massive charged particles’ Hawking radiation from a Reissner-Nordstrom-de Sitter (RNdS) black hole by Damour-Ruffini’s method. We get the unthermal spectrum when the back-reaction of particles’ energy and charge to spacetime is considered. The information will get out from the black hole with the corrected spectrum. The radiation is not exactly thermal and because the derivation obeys conservation laws, the non thermal Hawking radiation can carry information from the black hol

Recently, Hawking radiation of the black hole has been studied using the tunnel effect method. It is found that the radiation spectrum of the black hole is not a strictly pure thermal spectrum. How does the departure from pure thermal spectrum affect the entropy? This is a very interesting problem. In this paper, we calculate the partition function by energy spectrum obtained from tunnel effect. Using the partition function, we compute the black hole entropy and derive the expression of the black hole entropy after considering the radiation. And we derive the entropy of charged black hole. In our calculation, we consider not only the correction to the black hole entropy due to fluctuation of energy but also the effect of the change of the black hole charges on entropy. There is no other hypothesis. Our result is more reasonable.According to the fact that the black hole entropy is not divergent, we obtain the lower limit of Banados-Teitelboim-Zanelli black hole energy. That is, the least energy of Banados-Teitelboim-Zanelli black hole, which satisfies the stationary condition in thermodynamics.