The Thermodynamics Of The Bardeen Black Hole In AdS Space

In order to study the properties of black holes,there is a simple and effective way which can compare to thermodynamics.Hawking and Page research Schwarzschild black holes in AdS space,and they propose the concept of Hawking-Page phase transition.After this,scientist regard cosmological constant as pressure,so more and more black holes phase transition was turned out.On the other hand,the argue about singularity is endless,and the singularity problem should be solved in the frame of quantum gravity.Since we do not have a developed quantum gravity yet,a thorough discussion on the singular black hole seems impossible.In this paper,we study the Bardeen black hole,one of the regular black hole,and we discuss the stability and phase transition of the Bardeen black hole by thermodynamics of black hole.Thermodynamics of the Bardeen black hole in AdS space are described in the T-r_h plane?The cut-off radius is read obviously from it.The cut-off radius is the minimal radius of the Bardeen black hole.We also compare extreme radius of the mass to cut-off radius,and we get that the background of the cosmos can influence the existence of the extreme mass of black hole.By studying the parameterg(interpreted as a gravitationally collapsed magnetic monopole arising in a specific form of nonlinear electrodynamics)in Bardeen black hole carefully,we present each different value of parameter shows different phenomenon.The stability of Bardeen black hole is researched by Gibbs free energy and the heat capacity.And the phase transition is also discussed by the heat capacity.We calculate a critical value of g_m.When g g_m,there is second order phase transitions.While g>g_m,there is no second order phase transition.And we also find some problem which can be investigated in the future.