The extended uncertainty principle effects on the phase transitions of Reissner-Nordstr\"{o}m and Schwarzschild black holes

Abstract

In this paper, we investigate the phase transitions of Reissner-Nordstr\"{o}m (RN) and Schwarzschild black holes for the extended uncertainty principle (EUP) framework. Considering temperature $T$, charge $Q$ and electric potential $\Phi $ as the state parameters, we show the van der Waals (vdW) like phase transition of RN black hole in $Q-\Phi $ diagrams and find the critical points depending on EUP parameter $\alpha $. Furthermore, we find Hawking-Page like phase transition for Schwarzschild black hole. The results imply that the black holes in asymptotically flat space have the similar phase structure with the black holes in anti-de Sitter (AdS) space.