A general framework to study the extremal phase transition of black holes

Abstract

We investigate the universality of some features for the extremal phase transition of black holes and unify all the approaches which have been applied in different spacetimes. Unlike the other existing approaches where the information of the spacetime and its dimension is directly used to get various results, we provide a general formulation in which those results are obtained for any arbitrary black hole spacetime having an extremal limit. Calculating the second order moments of fluctuations of some thermodynamic quantities we show that, the phase transition occurs only in the microcanonical ensemble. Without considering any specific black hole we calculate the values of critical exponents for this type of phase transition. These are shown to be in agreement with the values obtained earlier for metric specified cases. Finally we extend our analysis to the geometrothermodynamics (henceforth GTD) formulation. We show that for any black hole, if there is an extremal point, the Ricci scalar for the Ruppeiner metric must diverge at that point.

24 Pages, No figure, New comments added, To appear in Phys. Rev. D

References in corpus (11)

• Geometrothermodynamics
• Geometrothermodynamics of black holes
• Unified geometric description of black hole thermodynamics
• Geometric description of BTZ black holes thermodynamics
• Van der Waals criticality in AdS black holes: a phenomenological study
• Thermogeometric phase transition in a unified framework
• Phase transition and critical phenomena of black holes: A general approach
• Continuous phase transition and critical behaviors of 3D black hole with torsion
• Phase transition and scaling behavior of topological charged black holes in Horava-Lifshitz gravity
• Microcanonical description of (micro) black holes
• Phantom black holes and critical phenomena