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Register a new userExtended Phase Space Thermodynamics for Black Holes in a Cavity
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In this paper, we extend the phase space of black holes enclosed by a spherical cavity of radius $r_{B}$ to include $Vequiv4pi r_{B}^{3}/3$ as a thermodynamic volume. The thermodynamic behavior of Schwarzschild and Reissner-Nordstrom (RN) black holes is then investigated in the extended phase space. In a canonical ensemble at constant pressure, we find that the aforementioned thermodynamic behavior is remarkably similar to that of the anti-de Sitter (AdS) counterparts with the cosmological constant being interpreted as a pressure. Specifically, a first-order Hawking-Page-like phase transition occurs for a Schwarzschild black hole in a cavity. The phase structure of a RN black hole in a cavity shows a strong resemblance to that of the van der Waals fluid. Our results may provide a new perspective for the extended thermodynamics of AdS black holes by analogy with black holes in a cavity.
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In this paper, we investigate the thermodynamics of dyonic black holes with the presence of power Maxwell electromagnetic field in the extended phase space, which includes the cosmological constant $Lambda$ as a thermodynamic variable. For a generic power Maxwell black hole with the electric charge and magnetic charge, the equation of state is given as the function of rescaled temperature $tilde{T}$ in terms of other rescaled variables $ tilde{r}_{+}$, $tilde{q}$ and $tilde{h}$, where $r_{+}$ is the horizon radius, $q$ is the electric charge and $h$ is some magnetic parameter. For some values of $tilde{q}$ and $tilde{h}$, the phase structure of the black hole is uniquely determined. Moreover the peculiarity of multiple temperature with some fixed parameter configurations results in more rich phase structures. Focusing on the power Maxwell Lagrangian with $mathcal{L} left( sright) =s^{2}$, we obtain the corresponding phase diagrams in the $ tilde{q}$-$tilde{h}$ plane, then analyse the black holes phase structure and critical behaviour. For this case, the critical line is semi-infinite and extends to $tilde{h}=infty$. We also examine thermal stabilities of these black holes.
Recently, the phase space of black holes in a spherical cavity of radius $r_{B}$ has been extended by introducing a thermodynamic volume $Vequiv4pi r_{B}^{3}/3$. In the extended phase space, we consider the thermodynamic geometry, which provides a powerful tool to understand the microscopic structure of black holes, of Reissner-Nordstr{o}m (RN) black holes in a cavity, as well as that of Reissner-Nordstr{o}m-AdS black holes. Although the phase structures of the cavity and AdS cases show striking resemblance, we find that there exist significant differences between the thermodynamic geometries of these two cases. In particular, a reentrant transition of the type of the microstructure interactions, i.e., repulsive $rightarrow$ attractive $rightarrow$ repulsive with increasing temperature in an isobaric process, is observed for RN black holes in a cavity.
Gravity is believed to have deep and inherent relation to thermodynamics. We study phase transition and critical behavior in the extended phase space of asymptotic anti de-Sitter (AdS) black holes in Einstein-Horndeski gravity. We demonstrate that the black hole in Einstein-Horndeski gravity undergo phase transition and P-V criticality mimicking the van der Waals gas-liquid system. The key approach in our study is to introduce a more reasonable pressure instead of previous pressure $P=-Lambda/8pi$ related to cosmological constant $Lambda$, and this proper pressure is given insight from the asymptotical behaviour of this black hole. Moreover, we also first obtain P-V criticality in the two cases with $Lambda=0$ and $Lambda>0$ in our paper, which implicates that the cosmological constant $Lambda$ may be not a necessary pressure candidate for black holes at the microscopic level. We present critical exponents for these phase transition processes.
Using the covariant phase space formalism, we compute the conserved charges for a solution, describing an accelerating and electrically charged Reissner-Nordstrom black hole. The metric is regular provided that the acceleration is driven by an external electric field, in spite of the usual string of the standard C-metric. The Smarr formula and the first law of black hole thermodynamics are fulfilled. The resulting mass has the same form of the Christodoulou-Ruffini mass formula. On the basis of these results, we can extrapolate the mass and thermodynamics of the rotating C-metric, which describes a Kerr-Newman-(A)dS black hole accelerated by a pulling string.
The $P$-$V$ phase transition and critical behavior in the extended phase space of asymptotic Anti-de Sitter (AdS) black holes have been widely investigated, in which four critical exponents around critical point are found to be consistent with values in mean field theory. Recently, another critical exponent $ u$ related to divergent correlation length at critical point has been investigated by using thermodynamic curvature scalar $R_N$ at critical point in charged AdS black hole. Moreover, one finds that the divergence behavior of $R_N$ at critical point indicates a universal property, i.e. characterized by a dimensionless constant that is identical to that for a van der Waals fluid. In this paper, we further check out this universal property through investigating thermodynamic curvature scalar in de Rham-Gabadadze-Tolley (dRGT) massive gravity, and find that this dimensionless constant is also indeed independent of horizon topology, massive graviton and dimension of spacetime. Furthermore, we investigate divergence behavior of thermodynamic curvature scalar at critical point in generic asymptotic Anti-de Sitter (AdS) black holes, and demonstrate the universality in this generic case. Those results give new insights into the microstructure of black holes.
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