Phase Transitions of GUP-Corrected Charged AdS Black Hole

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.

Microstructure of Charged AdS Black Hole with Minimal Length Effects

“…In addition, as anticipated by string theory and loop quantum gravity, the GUP modifies the usual Hawking temperature and Bekenstein-Hawking area law of entropy [54][55][56][57][58][59][60][61][62]. The significant influence of GUP on the black hole phase transitions has also been confirmed [63][64][65][66][67]. Considering the relation between thermodynamics and microstructures, we hope to find out what the underlying microstructure in a black hole with GUP effect is.…”

“…Based on the discussion in Ref. [65], the system can be classified into three different cases according to the value of α 2 /Q 2 : VdW-like PT Case: α 2 /Q 2 1. The system exhibits a typical VdW-like first-order phase transition, similar to the RN-AdS black hole.…”

Black hole thermodynamics under the generalized uncertainty principle and doubly special relativity

“…By defining the thermodynamic pressure as P = −Λ/8π, Then the surface gravity of the black hole is obtained as follows ref. [21]…”

Impacts of Generalized Uncertainty Principle on the Black Hole Thermodynamics and Phase Transition in a Cavity

“…More recently, the quantum gravity corrections to the thermodynamic phase transition and critical behavior of black holes have attracted a lot of attention [96][97][98][99][100][101][102]. In particular, when considering the effect of GUP, the modified thermodynamics of black holes in cavities are different from the original case, whereas the corresponding thermodynamic phase transition and critical behavior are similar to those of the AdS black hole [103,104]. Hence, those results may provide a new perspective on thermodynamic properties and evolution of black holes.…”