Thermodynamics of a Schwarzschild black hole surrounded by quintessence in the generalized uncertainty principle framework

TL;DR

This paper explores how the thermodynamics of a Schwarzschild black hole are affected by quintessence energy and generalized uncertainty principles, revealing modifications to temperature, entropy, and evaporation time.

Contribution

It introduces a framework combining quintessence with linear and quadratic generalized uncertainty principles to analyze black hole thermodynamics.

Findings

Entropy includes area, logarithmic, and inverse area corrections.

Quintessence parameter influences thermodynamic quantities.

Black hole evaporation time depends on quintessence and GUP parameters.

Abstract

We investigate the thermodynamics of a Schwarzschild black hole, surrounded by the quintessence energy-matter in the linear and quadratic generalized uncertainty principle framework. Considering the variance in the position to be of the order of the event horizon radius and equating the variance in the momentum to the Hawking temperature of the black hole, we substitute these variances in the deformed algebra. From there we obtained the generalized uncertainty principle-modified black hole temperature and eventually the specific heat of the black hole. Then we calculate the critical as well as the remnant mass and obtain the entropy relation. We observe that the entropy relation includes the usual leading order ``\textit{area divided by four}" term, sub-leading logarithmic term, and higher order inverse of the area corrections. Finally, calculating the energy output as a function of time, we obtain the evaporation time of the black hole. The results show the dependence of the quintessence parameter on the thermodynamic quantities in the framework of linear and quadratic generalized uncertainty principle.