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Register a new userThermodynamic Geometry of Black Holes Enclosed by a Cavity in Extended Phase Space
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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.
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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.
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.
By throwing a test charged particle into a Reissner-Nordstrom (RN) black hole, we test the validity of the first and second laws of thermodynamics and weak cosmic censorship conjecture (WCCC) with two types of boundary conditions, i.e., the asymptotically anti-de Sitter (AdS) space and a Dirichlet cavity wall placed in the asymptotically at space. For the RN-AdS black hole, the second law of thermodynamics is satisfied, and the WCCC is violated for both extremal and nearextremal black holes. For the RN black hole in a cavity, the entropy can either increase or decrease depending on the change in the charge, and WCCC is satisfied/violated for the extremal/nearextremal black hole. Our results indicate that there may be a connection between the black hole thermodynamics and the boundary condition imposed on the black hole.
We study the $P-V$ criticality and phase transition in the extended phase space of charged Gauss-Bonnet black holes in anti-de Sitter space, where the cosmological constant appears as a dynamical pressure of the system and its conjugate quantity is the thermodynamic volume of the black hole. The black holes can have a Ricci flat ($k=0$), spherical ($k=1$), or hyperbolic ($k=-1$) horizon. We find that for the Ricci flat and hyperbolic Gauss-Bonnet black holes, no $P-V$ criticality and phase transition appear, while for the black holes with a spherical horizon, even when the charge of the black hole is absent, the $P-V$ criticality and the small black hole/large black hole phase transition will appear, but it happens only in $d=5$ dimensions; when the charge does not vanish, the $P-V$ criticality and the small black hole/large phase transition always appear in $d=5$ dimensions; in the case of $dge 6$, to have the $P-V$ criticality and the small black hole/large black hole phase transition, there exists an upper bound for the parameter $b=widetilde{alpha}|Q|^{-2/(d-3)}$, where $tilde {alpha}$ is the Gauss-Bonnet coefficient and $Q$ is the charge of the black hole. We calculate the critical exponents at the critical point and find that for all cases, they are the same as those in the van der Waals liquid-gas system.
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.
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