Phantom black holes and critical phenomena

Abstract

We consider the two classes cosh and sinh of normal and phantom black holes of Einstein-Maxwelldilaton theory. The thermodynamics of these holes is characterized by heat capacities that may have both signs depending on the parameters of the theory. Leaving aside the normal Reissner-Nordström black hole, it is shown that only some phantom black holes of both classes exhibit critical phenomena. The two classes share a nonextremality, but special, critical point where the transition is continuous and the heat capacity, at constant charge, changes sign with an infinite discontinuity. This point yields a classification scheme for critical points. It is concluded that the two unstable and stable phases coexist on one side of the criticality state and disappear on the other side, that is, there is no configuration where only one phase exists. The sinh class has an extremality critical point where the entropy diverges. The transition from extremality to nonextremality with the charge held constant is accompanied by a loss of mass and an increase in the temperature. A special case of this transition is when the hole is isolated (microcanonical ensemble), it will evolve by emission of energy, which results in a decrease of its mass, to the final state of minimum mass and vanishing heat capacity. The Ehrenfest scheme of classification is inaccurate in this case but the generalized one due to Hilfer leads to conclude that the transition is of order less than unity. Fluctuations near criticality are also investigated.

General framework to study the extremal phase transition of black holes

“…The underlying motivation to pursue in this direction is to study various thermodynamic phenomena in terms of the geometric properties of the phase space of the system. For non-extremal black holes, there are two major approaches of studying the phase transition of black hole-one approach deals with the divergence of heat capacity and inverse of isothermal compressibility [31][32][33][34][35][36][37][38]. The other approach [39][40][41][42] is for the black holes in the AdS background, in which the cosmological constant is treated as the thermodynamic pressure.…”

Thermogeometric description of the van der Waals like phase transition in AdS black holes

“…[13,14]. While studying the phase transition of the black holes two approaches caught the attention of the physicists: one approach deals with the divergence of the heat ca- * krishnakanta@iitg.ernet.in † bibhas.majhi@iitg.ernet.in pacity and the inverse of the isothermal compressibility [15][16][17][18][19][20][21] and the other one discusses the phase transition of black holes in the AdS background with the cosmological constant being treated as the pressure. In the latter description the whole black hole system has been mapped to the van der Waals fluid system successfully in many avenues with the fact that the P -V diagram of the black holes at constant temperature and charges in the extended phase space looks exactly similar to the P -V diagram of the isotherms of the van der Waals gas system in the conventional thermodynamics.…”

AdS Black Hole with Phantom Scalar Field

“…For instance, the destiny of a black hole owing to accretion of phantom dark energy has been studied in [24]. Thermodynamics of spherically symmetric black holes and critical phenomenon with phantom Maxwell field and phantom scalar field have been discussed in [25]. Very recently, people have studied thermodynamical geometry of AdS charged black holes with spherical horizon in [26].…”