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Register a new userDivergence Behavior of Thermodynamic Curvature Scalar at Critical Point in the extended Phase Space of generic Black Holes
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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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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.
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.
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.
We study certain bi-scalar-tensor theories emanating from conformal symmetry requirements of Horndeskis four-dimensional action. The former scalar is a Galileon with shift symmetry whereas the latter scalar is adjusted to have a higher order conformal coupling. Employing technics from local Weyl geometry certain Galileon higher order terms are thus constructed to be conformally invariant. The combined shift and partial conformal symmetry of the action, allow us to construct exact black hole solutions. The black holes initially found are of planar horizon geometry embedded in anti de Sitter space and can accommodate electric charge. The conformally coupled scalar comes with an additional independent charge and it is well-defined on the horizon whereas additional regularity of the Galileon field is achieved allowing for time dependence. Guided by our results in adS space-time we then consider a higher order version of the BBMB action and construct asymptotically flat, regular, hairy black holes. The addition of the Galileon field is seen to cure the BBMB scalar horizon singularity while allowing for the presence of primary scalar hair seen as an independent integration constant along-side the mass of the black hole.
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