Thermal phase transitions of dimensionally continued AdS black holes

Abstract

We study the thermal phase transitions of charged black holes in dimensionally continued gravity in anti-de Sitter space. We find the van der Waals-like phase transition in the temperature-entropy plane of the black holes with spherical horizons in even dimensions, and there is no such phase transition of the black holes with flat and hyperbolic geometries. Near the critical inflection point, the critical exponent is computed and its value does not depend on the dimension. The Maxwell equal area law is checked to be fulfilled in the temperature-entropy diagram for the first order phase transition. In odd dimensions, there are no thermal phase transitions for the black hole with any geometry of the horizon.Comment: 18 pages, 2 figures; introduction extended, references adde

Thermogeometric study of van der Waals like phase transition in black holes: An alternative approach

“…In this case, while observing the criticality in the T − S plane (for example see Figure 1 of [21]), we consider only one charge (say Y ) while fixing the others. Therefore, in the thermogeometric manifold described by the metric g (1) ab , the T − S plane of thermodynamics will correspond to the thermogeometric S − Y plane described by the metric…”

“…In the AdS space, when the cosmological constant is regarded as the thermodynamic pressure [13][14][15][16][17], it was found that the P − V diagram of black holes in the extended phase space looks exactly similar to that of the ordinary thermodynamics [18,19], which implies a van der Waals phase transition in the black hole thermodynamics. Apart from the P − V criticality, there are also a few other criticalities in black hole space which also are of van der Waals type, like T − S criticality [20][21][22][23][24][25][26], Q − Φ criticality [27], Q 2 − Ψ criticality [28,29] etc. In addition, the van der Waals type phase transition has also been observed in [30], where the phase transition of black holes has been studied in AdS 5 × S 5 spacetime by considering the cosmological constant as the number of colors in the boundary gauge theory and its conjugate quantity as corresponding chemical potential.…”

Hairy black holes of Lovelock–Born–Infeld-scalar gravity

“…The coefficients a p in (4) are arbitrary constants, in the special case of DCG, the a p 's are chosen as [5,49]…”

“…Subsequently, thermal phase transitions of black holes in inverse temperature-horizon(1/T -r + ) plane and temperature-entropy(T -S) plane were studied in Refs. [45][46][47][48][49], it was found that the phase transition behaviors of the black holes resemble the ones of Van der Waals liquid-gas systems. Later on, by identify cosmological constant as pressure of the system [50], people studied thermal phase transitions of black holes in extended phase space and found Van der Waals-like phase transitions too [27,42,[51][52][53].…”

“…Because of the higher curvature terms in Lovelock gravity, the expression of pressure is highly nonlinear, which makes it very difficult to study phase transitions in extended phase space. On the other hand, it was argued that the thermal phase transitions of black holes in T -S plane and in P -V plane are dual to each other [49,56]. Thus in the following we will study thermal phase transitions of the black holes constructed below in T -S plane and see whether Van der Waals-like phase transitions or especially RTPs occur.…”