Huai-Fan Li

Hawking radiation and entropy correction of a black hole

Generalizing the method proposed by Damour-Ruffini for discussing the Hawking radiation of a black hole, under the condition that conversation of energy and the self-gravitation effects are considered, we obtain the radiation spectrum of the black hole. Our result is consistent with the result given by Parikh and Wilczek. It satisfies the unitary principle in quantum mechanics. The coefficient of the logarithmic term in correction to the Bekenstein-Hawking entropy of the black hole is derived.

On Thermodynamics of Charged and Rotating Asymptotically AdS Black Strings

In this paper, we study thermodynamics of cylindrically symmetric black holes and calculate the equation of states and heat capacity of charged and rotating black strings. In the process, we treat the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume. It is shown that, when taking the equivalence between the thermodynamic quantities of black strings and the ones of general thermodynamic system, the isothermal compressibility and heat capacity of black strings satisfy the stability conditions of thermodynamic equilibrium and no divergence points exist for heat capacity. Thus, we obtain the conclusion that the thermodynamic system relevant to black strings is stable and there is no second-order phase transition for AdS black holes in the cylindrically symmetric spacetime.

Entropy of Kerr–de Sitter black hole

Based on the consideration that the black hole horizon and the cosmological horizon of Kerr–de Sitter black hole are not independent of each other, we conjecture the total entropy of the system should have an extra term contributed from the correlations between the two horizons, except for the sum of the two horizon entropies. By employing globally effective first law and effective thermodynamic quantities, we obtain the corrected total entropy and find that the region of stable state for Kerr–de Sitter is related to the angular velocity parameter a, i.e., the region of stable state becomes bigger as the rotating parameters a is increases.

The critical phenomena of charged rotating de Sitter black holes

In this paper, we investigate the effective thermodynamic quantities in Kerr–Newman–de Sitter spacetime by considering the relations between the black hole event horizon and the cosmological event horizon. We find the effect of the critical point of Kerr–Newman–de Sitter spacetime for the different state parameters. We study the critical phenomena of the system taking different state parameters. This result is consistent with the nature of a liquid–gas phase transition at the critical point, hence deepening the understanding of the analogy of charged de Sitter spacetime and liquid–gas systems.

Entropy of Kerr-Newman Black Hole to All Orders in the Planck Length

Using the quantum statistical method, the difficulty of solving the wave equation on the background of the black hole is avoided.We directly solve the partition functions of Bose and Fermi field on the background of an axisymmetric Kerr-Newman black hole using the new equation of state density motivated by the generalized uncertainty principle in the quantum gravity. Then near the black hole horizon, we calculate entropies of Bose and Fermi field between the black hole horizon surface and the hypersurface with the same inherent radiation temperature measured by an observer at an infinite distance. In our results there are not cutoffs and little mass approximation introduced in the conventional brick-wall method. The series expansion of the black hole entropy is obtained. And this series is convergent. It provides a way for studying the quantum statistical entropy of a black hole in a non-spherical symmetric spacetime.

The Phase Transition of Higher Dimensional Charged Black Holes

We have studied phase transitions of higher dimensional charge black hole with spherical symmetry. We calculated the local energy and local temperature and find that these state parameters satisfy the first law of thermodynamics. We analyze the critical behavior of black hole thermodynamic system by taking state parameters of black hole thermodynamic system, in accordance with considering the state parameters of van der Waals system, respectively. We obtain the critical point of black hole thermodynamic system and find that the critical point is independent of the dual independent variables we selected. This result for asymptotically flat space is consistent with that for AdS spacetime and is intrinsic property of black hole thermodynamic system.

Clapeyron equation and phase equilibrium properties in higher dimensional charged topological dilaton AdS black holes with a nonlinear source

Using Maxwell’s equal area law, we discuss the phase transition of higher dimensional charged topological dilaton AdS black hole with a nonlinear source. The coexisting region of the two phases is found and we depict the coexistence region in the P–v diagrams. The two-phase equilibrium curves in the P–T diagrams are plotted, and we take the first order approximation of volume v in the calculation. To better compare with a general thermodynamic system, the Clapeyron equation is derived for a higher dimensional charged topological black hole with a nonlinear source. The latent heat of an isothermal phase transition is investigated. We also study the effect of the parameters of the black hole on the region of two-phase coexistence. The results show that the black hole may go through a small–large phase transition similar to those of usual non-gravity thermodynamic systems.

Maxwell’s equal area law for black holes in power Maxwell invariant

In this paper, we consider the phase transition of black hole in power Maxwell invariant by means of Maxwell’s equal area law. First, we review and study the analogy of nonlinear charged black hole solutions with the Van der Waals gas–liquid system in the extended phase space, and obtain isothermal P-v diagram. Then, using the Maxwell’s equal area law we study the phase transition of AdS black hole with different temperatures. Finally, we extend the method to the black hole in the canonical (grand canonical) ensemble in which charge (potential) is fixed at infinity. Interestingly, we find the phase transition occurs in the both ensembles. We also study the effect of the parameters of the black hole on the two-phase coexistence. The results show that the black hole may go through a small-large phase transition similar to those of usual non-gravity thermodynamic systems.

Quantized Space-Time and Black Hole Entropy

On the basis of Snyder’s idea of quantized space-time, we derive a new generalized uncertainty principle and a new modified density of states. Accordingly, we obtain a corrected black hole entropy with a logarithmic correction term by employing the new generalized uncertainty principle. In addition, we recalculate the entropy of spherically symmetric black holes using statistical mechanics. Because of the use of the minimal length in quantized space-time as a natural cutoff, the entanglement entropy we obtained does not have the usual form A/4 but has a coefficient dependent on the minimal length, which shows differences between black hole entropy in quantized space-time and that in continuous space-time.

Hawking and Unruh effects of the cosmological horizon in a higher-dimensional Kerr-de Sitter spacetime by the global embedding approach

With appropriately chosen parameters, there exist the black-hole horizon and the cosmological horizon in the higher-dimensional Kerr-de Sitter spacetime, where these two horizons generally have different Hawking temperatures. In this letter we first reduce the higher-dimensional Kerr-de Sitter spacetime line element to a 2-dimensional one (the (t−r) sector) using the dimensional reduction method near the cosmological horizon, and then investigate the Unruh/Hawking effects of the cosmological horizon by the global embedding approach.