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We discuss phase transition of the charged topological dilaton AdS black holes by Maxwell equal area law. The two phases involved in the phase transition could coexist and we depict the coexistence region in P-v diagrams. The two-phase equilibrium curves in P-T diagrams are plotted, the Clapeyron equation for the black hole is derived, and the latent heat of isothermal phase transition is investigated. We also analyze the parameters of the black hole that could have an effect on the two-phase coexistence. The results show that the black holes may go through a small-large phase transition similar to that of a usual nongravity thermodynamic system. [ABSTRACT FROM AUTHOR]

In this paper, by analyzing the thermodynamic properties of charged AdS black hole and asymptotically flat space-time charged black hole in the vicinity of the critical point, we establish the correspondence between the thermodynamic parameters of asymptotically flat space-time and nonasymptotically flat space-time, based on the equality of black hole horizon area in the two different types of space-time. The relationship between the cavity radius (which is introduced in the study of asymptotically flat space-time charged black holes) and the cosmological constant (which is introduced in the study of nonasymptotically flat space-time) is determined. The establishment of the correspondence between the thermodynamics parameters in two different types of space-time is beneficial to the mutual promotion of different time-space black hole research, which is helpful to understand the thermodynamics and quantum properties of black hole in space-time. [ABSTRACT FROM AUTHOR]

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 (Q,Φ) of black hole thermodynamic system, in accordance with considering the state parameters (P,V) 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. [ABSTRACT FROM AUTHOR]

We study the phase transition of charged Gauss-Bonnet-de Sitter (GB-dS) black hole. For black holes in de Sitter spacetime, there is not only black hole horizon, but also cosmological horizon. The thermodynamic quantities on both horizons satisfy the first law of the black hole thermodynamics, respectively; moreover, there are additional connections between them. Using the effective temperature approach, we obtained the effective thermodynamic quantities of charged GB-dS black hole. According to Ehrenfest classification, we calculate some response functions and plot their figures, from which one can see that the spacetime undergoes a second-order phase transition at the critical point. It is shown that the critical values of effective temperature and pressure decrease with the increase of the value of GB parameter α. [ABSTRACT FROM AUTHOR]