Thermodynamics of the Reissner-Nordstr\"om black hole with quintessence matter on the EGUP framework

TL;DR

This paper explores quantum corrections to the thermodynamics of Reissner-Nordström black holes with quintessence matter, analyzing effects on temperature, entropy, and phase behavior within the EGUP framework.

Contribution

It introduces modified thermodynamic functions considering quantum corrections and the influence of quintessence matter within the EGUP framework, highlighting the roles of normalization and correction parameters.

Findings

Horizon radius lower bound affects Hawking temperature.

Parameter η₀ influences heat capacity thresholds.

Entropy correction is independent of quintessence matter.

Abstract

In this paper, we investigate the quantum correction on thermodynamics of the Reissner-Nordstr\"om black hole in the presence of the quintessence matter associated with dark energy. To this end, the modified Hawking temperature, heat capacity, and entropy functions of the black hole are derived. { Investigation reveals that the modified uncertainty principles and normalization factor $\alpha$ restrict the lower bound value of horizon radius to affect the Hawking temperature and the parameter $\eta_{0}$ have a non-negligible effect on the heat capacity threshold.} {Furthermore}, the correction of entropy does not depend on the quintessence matter. It is also examined the equation of state associated with the pressure and the volume in this framework. In addition, we employ graphical methods to compare and discuss the findings within the generalized uncertainty principle (GUP) and extended uncertainty principle (EUP).