Thermodynamics of Schwarzschild black hole surrounded by quintessence with generalized uncertainty principle

TL;DR

This paper explores how a generalized uncertainty principle affects the thermodynamics of Schwarzschild black holes surrounded by quintessence, revealing bounds and quantum deformation effects on thermodynamic functions.

Contribution

It introduces a deformation of the Heisenberg algebra to study quantum effects on black hole thermodynamics in a quintessence environment, deriving new thermodynamic bounds and equations.

Findings

Bounds on temperature, entropy, and heat capacity due to quintessence and deformation

Corrected density and equation of state for quintessence matter

Quantum deformation influences thermodynamic properties and bounds

Abstract

In this manuscript, we consider a deformation on the Heisenberg algebra and investigate the effects on the thermodynamics of the Schwarzschild black hole that is surrounded by quintessence matter. To this end, we obtain the temperature, entropy, and heat capacity functions of the black hole by using the standard laws of thermodynamic according to the considered deformation. We show that upper and lower bound values appear on these functions based on the quintessence and deformed algebra. Then, we derive the corrected density of quintessence matter and the black hole's equation of state functions. We compare these results with the standard Schwarzschild black hole with and without quintessence with the graphical methods and interpret the quantum deformation effects.