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

TL;DR

This paper explores how the extended uncertainty principle influences phase transitions in Reissner-Nordström and Schwarzschild black holes, revealing vdW-like and Hawking-Page-like transitions and their dependence on EUP parameters.

Contribution

It demonstrates the impact of the extended uncertainty principle on black hole phase transitions, connecting flat space black holes to AdS-like phase structures.

Findings

Reissner-Nordström black holes exhibit vdW-like phase transitions in Q-Φ diagrams.

Critical points depend on the EUP parameter α.

Schwarzschild black holes show Hawking-Page-like phase transitions.

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.