We study the thermodynamics of D-dimensional Born-Infeld AdS black holes in the extended phase space. We find that the usual small-large black hole phase transition, which exhibits analogy with the Van de Waals liquid-gas system, holds in all dimensions greater than three. However, different from the four-dimensional case, in the system of higher dimensional Born-Infeld AdS black holes there is no reentrant phase transition. For the three-dimensional Born-Infeld AS black hole, there does not exist critical phenomena.

Abstract:We calculate the quasinormal modes of massless scalar perturbations around small and large four-dimensional Reissner-Nordstrom-Anti de Sitter (RN-AdS) black holes. We find a dramatic change in the slopes of quasinormal frequencies in small and large black holes near the critical point where the Van der Waals like thermodynamic phase transition happens. This further supports that the quasinormal mode can be a dynamic probe of the thermodynamic phase transition.

We study the P − V criticality and phase transition in the extended phase space of anti-de Sitter (AdS) black holes in higher-dimensional de Rham, Gabadadze and Tolley (dRGT) massive gravity, treating the cosmological constant as pressure and the corresponding conjugate quantity is interpreted as thermodynamic volume. Besides the usual small/large black hole phase transitions, the interesting thermodynamic phenomena of reentrant phase transitions (RPTs) are observed for black holes in all d ≥ 6-dimensional spacetime when the coupling coefficients c i m 2 of massive potential satisfy some certain conditions.

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The scalarization of Reissner-Nordström black holes was recently proposed in the Einstein-Maxwell-scalar theory. Here, we show that the appearance of the scalarized Reissner-Nordström black hole is closely related to the Gregory-Laflamme instability of the Reissner-Nordström black hole without scalar hair.

Introducing a new form of scalar potential V (φ), we derive a proper form of the rotating black hole solution in three-dimensional Einstein gravity with nonminimally coupled scalar field and find that the first law of thermodynamics of this new rotating hairy black hole can be protected, where the scalar field parameter B is constrained to relate to the black hole size. We also disclose the Hawking-Page phase transition between this rotating hairy black holes and the pure thermal radiation. Moreover, we study phase transitions between this rotating hairy black hole and rotating BTZ black hole. Considering the matchings for the temperature and angular momentum, we find that the rotating BTZ black hole always has smaller free energy which is a thermodynamically more preferred phase. Additionally, we evaluate the thermodynamics of the rotating black hole with minimally coupled scalar hair in three dimensions, which exhibits that the thermodynamical behaviors of this rotating hairy black hole are very similar to those of the rotating black hole with nonminimally coupled scalar hair.

We study the thermodynamics in the grand canonical ensemble of D-dimensional charged Gauss-Bonnet-AdS black holes in the extended phase space. We find that the usual smalllarge black hole phase transition, which exhibits analogy with the Van de Waals liquid-gas system holds in five-dimensional spherical charged Gauss-Bonnet-AdS black holes when its potential is fixed within the range 0 < Φ < √ 3π 4 . For the other higher dimensional and topological charged Gauss-Bonnet-AdS black holes, there is no such phase transition. In the limiting case, Reissner-Nordstrom-AdS black holes, with vanishing Gauss-Bonnet parameter, there is no critical behavior in the grand canonical ensemble. This result holds independent of the spacetime dimensions and topologies. We also examine the behavior of physical quantities in the vicinity of the critical point in the five-dimensional spherical charged Gauss-BonnetAdS black holes.

We study the scalarized charged black holes in the Einstein-Maxwell-Scalar (EMS) theory with scalar mass term. In this work, the scalar mass term is chosen to be m 2 φ = α/β, where α is a coupling parameter and β is a mass-like parameter. It turns out that any scalarized charged black holes are not allowed for the case of β ≤ 4.4 because this case implies the stable Reissner-Nodström (RN) black holes. In the massless limit of β → ∞, one recovers the case of the EMS theory. We note that the unstable RN black hole implies the appearance of scalarized charged black holes. The other unstable case of β > 4.4 allows us to obtain the n = 0, 1, 2, · · · scalaized charged black holes for α(β) ≥ α th (β) where α th (β) represents the threshold of instability for the RN black hole. Furthermore, it is shown that the n = 0 black hole is stable against radial perturbations, while the n = 1 black hole is unstable. This stability result is independent of the mass parameter β.