Thermodynamics And Joule-Thomson Expansion Of The Bardeen-AdS Black Holes

The discovery of black hole thermodynamics reveals that there is a deep relationship be-tween the gravitational system and the thermodynamic system.Specially,when we consider the cosmological constant?as the the thermodynamic pressure and the mass as the enthalpy of the thermodynamic system,the law of thermodynamics of anti-de Sitter(AdS)black holes,which is just like the law of ordinary thermodynamic system,is obtained.More and more phase structure of black holes has been found along with the research,such as the P-v critical phenomenon,the triple point and the heat engine process,etc.In addition,¨Okc¨u and Ayd?ner studied the Joule-Thomson expansion process of the charged AdS black holes until recently.In this paper,we will also consider the cosmological constant?as the the thermodynamic pres-sure to research the phase structure,Joule-Thomson expansion process and the Ruppeiner scalar curvature in the Bardeen-AdS black holes.We first get the metric of Bardeen-AdS black holes by adding the cosmological constant?term to the action given by Ay?on-Beato and Garc??a,and get the minimum radius of black holes.Then we plot the isotherm in pressure-volume diagram to study the P-v critical phase transition of the Bardeen-AdS black holes.The swallow tail behavior of the Gibbs free energy have been also found.So the Bardeen-AdS black holes have the similar thermodynamic property with Van der Waals system.The thermodynamic stability and phase structure of the Bardeen-AdS black holes have been also discussed by the specific heat at constant pressure.Then we study the Joule-Thomson expansion process of the Bardeen-AdS black holes,and find that the inversion curve is a non-closed curve which is different from Van der Waals system.An interesting phenomenon is that the isenthalpic curve of some Bardeen-AdS holes does not have the critical point.Moreover the mass of this Bardeen-AdS black hole is also below the minimum inversion mass with the same magnetic charge.These all mean that the black hole may be always in heating process.Finally,we calculate the Ruppeiner scalar curvature in the reduced parameter space.It is found that the extreme black hole with zero temperature has a Ruppeiner scalar curvature of~12,which is the same with other black holes.This may mean that extreme black holes have the same microscopic property.The divergence of Ruppeiner scalar curvature have been also discussed.Moreover,the Ruppeiner scalar curvature is greater than zero only in the case of small Bardeen-AdS black holes,implying that repulsive interactions dominate among the black hole microstructures.