Phantom black holes and critical phenomena

TL;DR

This paper analyzes the thermodynamics and critical phenomena of phantom black holes in Einstein-Maxwell-dilaton theory, revealing unique phase transitions, critical points, and stability properties that differ from classical black holes.

Contribution

It identifies and classifies critical points in phantom black holes, showing their thermodynamic behavior and phase transitions, extending understanding beyond normal black hole models.

Findings

Certain phantom black holes exhibit critical phenomena with continuous transitions.

A classification scheme for critical points based on heat capacity behavior is proposed.

Transitions can be of order less than unity, indicating complex phase behavior.

Abstract

We consider the two classes cosh and sinh of normal and phantom black holes of Einstein-Maxwell-dilaton 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-Nordstr\"om 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.