The effect of modified dispersion relations on the thermodynamics of Schwarzschild black hole surrounded by quintessence

TL;DR

This paper explores how modified dispersion relations and quintessence matter influence the thermodynamics, stability, and horizon bounds of Schwarzschild black holes, revealing potential remnants and stability conditions.

Contribution

It introduces the combined effects of MDR and quintessence matter on black hole thermodynamics, highlighting new bounds and stability criteria.

Findings

MDR-correction imposes the same lower bound on the horizon.

Quintessence matter sets an upper bound depending on the state parameter.

Black hole stability depends solely on the modified dispersion relation.

Abstract

In this manuscript, we investigate the effects of a modified dispersion relation on the thermodynamics of Schwarzschild black hole surrounded by the quintessence matter. We find that the MDR-correction states the same lower bound on the horizon, while the quintessence matter specifies the upper bound to the horizon depending on the state parameter. Due to MDR-correction and quintessence matter presence, we observe modifications in equation of state and specific heat functions of black hole. We show that a remnant can occur according to quintessence matter, and the black hole's stability depends only on the modified dispersion relation.