Criticality Of AdS Black Holes Research Articles

P-V criticality of AdS black holes in a general framework

In black hole thermodynamics, it has been observed that AdS black holes behave as van der Waals system if one interprets the cosmological constant as a pressure term. Also the critical exponents for the phase transition of AdS black holes and the van der Waals systems are same. Till now this type of analysis is done by two steps. In the first step one shows that a particular metric allows phase transition and in the second step, using this information, one calculates the exponents. Here, we present a different approach based on two universal inputs (the general forms of the Smarr formula and the first law of thermodynamics) and one assumption regarding the existence of van der Waals like critical point for a metric. We find that the same values of the critical exponents can be obtained by this approach. Thus we demonstrate that, though the existence of van der Waals like phase transition depends on specific metrics, the values of critical exponents are then fixed for that set of metrics.

Ehrenfest scheme forP−Vcriticality of higher dimensional charged black holes, rotating black holes, and Gauss-Bonnet AdS black holes

To provide an analytic verification of the nature of phase transition at the critical point of $P-V$ criticality, the original expressions of Ehrenfest equations have been introduced directly. By treating the cosmological constant and its conjugate quantity as thermodynamic pressure and volume respectively, we carry out analytical check of classical Ehrenfest equations. To show that our approach is universal, we investigate not only higher-dimensional charged AdS black holes, but also rotating AdS black holes. Not only are the examples of Einstein gravity shown, but also the example of modified gravity is presented for Gauss-Bonnet AdS black holes. The specific heat at constant pressure $C_P$, the volume expansion coefficient $\alpha$ and the isothermal compressibility coefficient $\kappa_T$ are found to diverge exactly at the critical point. It has been verified that both Ehrenfest equations hold at the critical point of $P-V$ criticality in the extended phase spaces of AdS black holes. So the nature of the critical point of $P-V$ criticality of AdS black holes has been demonstrated analytically to be a second-order phase transition. These results are consistent with the nature of liquid-gas phase transition at the critical point. In this sense, our research would deepen the understanding of the relations of AdS black holes and liquid-gas systems. Moreover, our successful approaches to introduce the original expressions of Erhenfest equations directly into black hole phase transition research demonstrate again that black hole thermodynamics is closely related to classical thermodynamics, which allows us to borrow techniques from classical thermodynamics to investigate the thermodynamics of black holes.

Another novel Ehrenfest scheme for [formula omitted] criticality of RN-AdS black holes

In this Letter, we explore another novel Ehrenfest scheme which can also be utilized in the P–V criticality research of RN-AdS black holes. The novel form of Ehrenfest scheme is neither the one in classical thermodynamics nor the analogy one proposed for grand-canonical ensemble in literatures. After a detailed derivation of the novel Ehrenfest equations, an analytical check is carried out at the critical point of P–V criticality of RN-AdS black holes. It is shown once again that the phase transition at the critical point is a second order one. Both the novel Ehrenfest scheme developed in this Letter and the classical Ehrenfest equations utilized in our former research can be applied to investigate the nature of phase transition at the critical point of P–V criticality of AdS black holes.

Ehrenfest scheme for the extended phase space of f(R) black holes

In this letter, the original expressions of Erhenfest equations have been introduced directly into the black-hole research by treating the cosmological constant and its conjugate quantity as thermodynamic pressure and volume, respectively. The nature of phase transition at the critical point of criticality of AdS black holes in f(R) gravity has been investigated as an example. The specific heat at constant pressure CP, the volume expansion coefficient α and the isothermal compressibility coefficient are found to diverge at the critical point. An analytical check of Ehrenfest equations has been carried out and it has been proved that both Ehrenfest equations are satisfied. So AdS black holes in f(R) gravity undergo a second-order phase transition at the critical point. This result is consistent with the nature of liquid-gas phase transition at the critical point and would help deepen the understanding of the relations between AdS black holes and liquid-gas system. Moreover, the influences of f(R) correction on the thermodynamics and the phase transition of AdS black holes in f(R) gravity have also been shown in this letter.