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We study the thermodynamic stabilities of uncharged and charged black holes surrounded by quintessence (BHQ) by means of effective thermodynamic quantities. When the state parameter of quintessence $$\omega _q$$ is appropriately chosen, the structures of BHQ are something like that of black holes in de Sitter space. Constructing the effective first law of thermodynamics in two different ways, we can derive the effective thermodynamic quantities of BHQ. Especially, these effective thermodynamic quantities also satisfy Smarr-like formulae. It is found that the uncharged BHQ is always thermodynamically unstable due to negative heat capacity, while for the charged BHQ there are phase transitions of the second order. We also show that there are several differences on the thermodynamic properties and critical behaviors of BHQ between the two ways we employed. [ABSTRACT FROM AUTHOR]

By use of the Jacobi determinant, we verify that, for a thermodynamic system which satisfies the first law of thermodynamics, if only there is second-order phase transition in the system, the Prigogine-Defay ratio is the constant 1. This conclusion is universal and independent of the concrete forms of the thermodynamic functions and also apply to black holes. [ABSTRACT FROM AUTHOR]

In this paper, we study the phase structure and equilibrium state space geometry of charged topological dilaton black holes in ( n+1)-dimensional anti-de Sitter spacetime. By considering the pairs of parameters ( P∼ V) and ( Q∼ U) as variables, we analyze the phase structure and critical phenomena of black holes and discuss the relation between the two kinds of critical phenomena. We find that the phase structures and critical phenomena drastically depend on the cosmological constant l (or the static electric charge Q of the black holes), dimensionality n and dilaton field Φ. [ABSTRACT FROM AUTHOR]

Recently, the Hawking radiation of a black hole has been studied using the tunnel effect method. The radiation spectrum of a black hole is derived. By discussing the correction to spectrum of the rotating black hole, we obtain the canonical entropy. The derived canonical entropy is equal to the sum of Bekenstein-Hawking entropy and correction term. The correction term near the critical point is different from the one near others. This difference plays an important role in studying the phase transition of the black hole. The black hole thermal capacity diverges at the critical point. However, the canonical entropy is not a complex number at this point. Thus we think that the phase transition created by this critical point is the second order phase transition. The discussed black hole is a five-dimensional Kerr-AdS black hole. We provide a basis for discussing thermodynamic properties of a higher-dimensional rotating black hole. [ABSTRACT FROM AUTHOR]

Since the black hole and cosmological horizons in the de Sitter (dS) spacetime with the Reissner–Nordström (RN) black hole are not independent with each other, which is caused by the gravitational effect, the interplay between two horizons should be considered. Based on this, by introducing the interactive entropy the RN–dS spacetime is analogous to a thermodynamic system with various thermodynamic quantities, in which the laws of thermodynamics still hold on. In our work, the thermodynamic properties of the RN–dS spacetime are mapped out in the induced phase space, which are similar to that in AdS black holes. The phase transition of the RN–dS spacetime between the high-potential and the low-potential black hole phases is observed. Compared with an ordinary thermodynamic system, the similar behaviors about the Joule–Thomson expansion and the critical exponents are also checked out. Finally, the scalar curvatures of two existent phases are presented to reveal the underlying microstructure and nature of phase transition in the RN–dS spacetime, which opens a new window to investigate the dS spacetime with black holes from an observational perspective. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the combined effects of the cloud of strings and quintessence on the thermodynamics of a Reissner–Nordström–de Sitter black hole. Based on the equivalent thermodynamic quantities considering the correlation between the black hole horizon and the cosmological horizon, we extensively discuss the phase transitions of the spacetime. Our analysis proves that similar to the case in AdS spacetime, second-order phase transitions could take place under certain conditions, with the absence of first-order phase transition in the charged de Sitter (dS) black holes with cloud of string and quintessence. The effects of different thermodynamic quantities on the phase transitions are also quantitatively discussed, which provides a new approach to study the thermodynamic qualities of unstable dS spacetime. Focusing on the entropy force generated by the interaction between the black hole horizon and the cosmological horizon, as well as the Lennard–Jones force between two particles, our results demonstrate the strong degeneracy between the entropy force of the two horizons and the ratio of the horizon positions, which follows the surprisingly similar law given the relation between the Lennard–Jones force and the ratio of two particle positions. Therefore, the study of the entropy force between two horizons is not only beneficial to the deep exploration of the three modes of cosmic evolution, but also helpful to understand the correlation between the microstates of particles in black holes and those in ordinary thermodynamic systems. [ABSTRACT FROM AUTHOR]

On the belief that a black hole is a thermodynamic system, we study the phase transition of nonsingular black holes. If the black hole entropy takes the form of the Bekenstein—Hawking area law, the black hole mass M is no longer the internal energy of the black hole thermodynamic system. Using the thermodynamic quantities, we calculate the heat capacity, thermodynamic curvature and free energy. It is shown that there will be a larger black hole/smaller black hole phase transition for the nonsingular black hole. At the critical point, the second-order phase transition appears. [ABSTRACT FROM AUTHOR]

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]

Previously, the Maxwell equal-area law has been used to discuss the conditions satisfied by the phase transition of charged AdS black holes with cloud of string and quintessence, and it was concluded that black holes have phase transition similar to that of vdW system. The phase transition depends on the electric potential of the black hole and is not the one between a large black hole and a small black hole. On the basis of this result, we study the relation between the latent heat of the phase transition and the parameter of dark energy, and use the Landau continuous phase transition theory to discuss the critical phenomenon of the black hole with quintessence and give the critical exponent. By introducing the number density of the black hole molecules, some properties of the microstructure of black holes are studied in terms of a phase transition. It is found that the electric charge of the black hole and the normalization parameter related to the density of quintessence field play a key role in the phase transition. By constructing the binary fluid model of the black hole molecules, we also discuss the microstructure of charged AdS black holes with a cloud of strings and quintessence. [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]

After introducing the connection between the black hole horizon and the cosmological horizon, we discuss the thermodynamic properties of Reissner-Nordström-de Sitter (RN-dS) space-time. We present the condition under which RN-dS black hole can exist. Employing Ehrenfest' classification, we conclude that the phase transition of RN-dS black hole is the second-order one. The position of the phase transition point is irrelevant to the electric charge of the system. It only depends on the ratio of the black hole horizon and the cosmological horizon. [ABSTRACT FROM AUTHOR]