Abstract
We study the thermodynamic properties and critical behaviors of the topological charged black hole in AdS space under the consideration of the generalized uncertainty principle (GUP). It is found that only in the spherical horizon case there are Van der Waals-like first-order phase transitions and reentrant phase transitions. From the equation of state we find that the GUP-corrected black hole can have one, two, and three apparent critical points under different conditions. However, it is verified by the Gibbs free energy that in either case there is at most one physical critical point.
Highlights
Since Hawking-Page phase transition of Schwarzschild-AdS black hole was explored in [1], phase structures and critical behaviors of various black holes in AdS space have been extensively studied [2,3,4,5,6,7,8,9,10,11,12,13]
In [2, 3], the Van der Waals (VdW)-like first-order phase transition was first found in the RN-AdS black hole, in the extended phase space it was found that the critical behaviors of the RN-AdS black hole have more similarities to that of the VdW liquid/gas system [16]
On the basis of this relation, the corrected temperature and entropy for some static and stationary black holes were given in [46]. Using these corrected thermodynamic quantities, we have studied the critical behaviors of the Schwarzschild-AdS black hole and the RN-AdS black hole in [47]
Summary
Since Hawking-Page phase transition of Schwarzschild-AdS black hole was explored in [1], phase structures and critical behaviors of various black holes in AdS space have been extensively studied [2,3,4,5,6,7,8,9,10,11,12,13]. In [2, 3], the Van der Waals (VdW)-like first-order phase transition was first found in the RN-AdS black hole, in the extended phase space it was found that the critical behaviors of the RN-AdS black hole have more similarities to that of the VdW liquid/gas system [16]. On the basis of this relation, the corrected temperature and entropy for some static and stationary black holes were given in [46] Using these corrected thermodynamic quantities, we have studied the critical behaviors of the Schwarzschild-AdS black hole and the RN-AdS black hole in [47]. We will further study the critical behaviors and phase transitions of the corrected charged topological AdS black hole in the extended phase space.
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