Microstructure of Charged AdS Black Hole with Minimal Length Effects

Abstract

In this work, the microstructure of charged AdS black holes under minimal length effects is investigated. We study the thermodynamics of black holes in the extended phase space, where the cosmological constant is regarded as the thermodynamic pressure. The modified Hawking temperature and phase transition are obtained based on the generalized uncertainty principle (GUP). Then, using thermodynamic geometry, we show that the microstructure of black holes can be determined by the ratio of GUP parameter to charge. For a small ratio, the black hole exhibits the typical RN-AdS microstructure with van der Waals phase transition and repulsive/attractive interactions. As the ratio increases, the reentrant phase transition takes place, and both the repulsion-attraction coexisted black hole and the attraction dominated black hole can be found in this case. For a large ratio, the black hole behaves like a Schwarzchild-AdS black hole in which neither phase transition nor repulsive interaction exists. These results suggest that the GUP effect will reduce the repulsive interaction presented by the charged AdS black hole, which can also be qualitatively understood from the perspective of black hole molecules.