Abstract
In the present paper we try to connect the Bardeen black hole with the concept of the recently proposed black hole chemistry. We study thermodynamic properties of the regular black hole with an anti-deSitter background. The negative cosmological constant Λ plays the role of the positive thermodynamic pressure of the system. After studying the thermodynamic variables, we derive the corresponding equation of state and we show that a neutral Bardeen-anti-deSitter black hole has similar phenomenology to the chemical Van der Waals fluid. This is equivalent to saying that the system exhibits criticality and a first order small/large black hole phase transition reminiscent of the liquid/gas coexistence.
Highlights
Black holes are among the most fascinating and mysterious astrophysical objects, predicted theoretically in the context of general relativity (GR)
We derive the corresponding equation of state and we show that the black hole appears a first order phase transition between small/large black hole, along with a P –V criticality with critical exponents identical to those of a Van der Waals gas
We have presented a geometric and thermodynamic analysis of the Bardeen black hole inside an extended AdS phase space
Summary
Black holes are among the most fascinating and mysterious astrophysical objects, predicted theoretically in the context of general relativity (GR). One of the most successful theories is the AdS/CFT duality [3,4] which relates AdS gravitational theories to conformal field theories formulated on a boundary Another recent interesting proposal [5] is the treatment of the negative cosmological constant of an AdS background as a thermodynamic variable related to the positive pressure P of the system through the relation. Bardeen black hole is a spherically symmetric solution resulting from Einstein equations in the presence of a nonlinear electromagnetic field coupled to matter [30] It is parametrized by two quantities; a mass M and a charge q both having dimensions of length in geometric units (c = G = 1).
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