Thermodynamic modifications to Bardeen black holes surrounded by quintessence based on the new higher order GUP

TL;DR

This work investigates thermodynamic corrections to a regular Bardeen black hole surrounded by quintessence under a new higher-order GUP controlled by the deformation parameter $β$. The authors derive a GUP-corrected Hawking temperature $T_{GUP}$, entropy $S_{GUP}$, and heat capacity $C_{GUP}$, together with remnant temperature $T_{rem}$ and remnant mass $M_{rem}$, and show how quintessence influences these quantities via the horizon radius $r_H$. They also formulate a $P$–$V$-type equation of state $P_{GUP}(V)$ and analyze how both $β$ and the quintessence parameter $w_q$ shape the isotherms, especially at small $r_H$, indicating the possibility of black-hole remnants and altered evaporation dynamics. The results indicate that GUP can yield black-hole remnants and that the thermodynamic behavior is sensitively affected by the interplay between quantum gravity corrections and dark-energy surroundings.

Abstract

In this article, the thermodynamic properties of Bardeen black holes surrounded by quintessence are investigated in the framework of a new higher order GUP. The modified Hawking temperature, entropy and heat capacity are derived using a heuristic approach. Meanwhile, the remnant temperature and mass are deduced, and the modified black hole state equation is obtained by utilizing the energy density of matter. Ultimately, we analyze the effects of the GUP controlling deformation parameter $β$ on these thermodynamic properties using graphical illustrations, to more comprehensively understand the thermodynamic behavior of the black hole in the context of higher order GUP.

Figures (5)

• Figure 1: The behavior between $f (r)$ and $r$ when $\alpha=0,w_q=-1/3$ and $w_q=-2/3$.
• Figure 2: The behavior between $T_{GUP}$ and $r_H$ for different parameters $\beta$$( \alpha =0.1, g=0.2)$.
• Figure 3: The behavior between $M_{rem}$ and $\beta$ for different parameters $w_q$.
• Figure 4: The behavior between $C_{GUP}$ and $r_H$ for different parameters $\beta$$( \alpha =0.1, g=0.2)$.
• Figure 5: The behavior between $P_{GUP}$ and $r_H$ for different parameters $\beta$$(g = 0. 002)$.