Corrected thermodynamics of $(2+1)D$ black hole conformally coupled to a massless scalar

TL;DR

This paper investigates how thermal fluctuations influence the entropy and stability of small conformally dressed black holes in three dimensions, revealing significant effects on thermodynamics and stability.

Contribution

It provides a detailed analysis of corrected entropy and thermodynamic variables for (2+1)D conformal black holes, highlighting the impact of thermal fluctuations on small black hole stability.

Findings

Thermal fluctuations significantly alter entropy for small black holes.

Instability arises in small black holes due to thermal fluctuations.

Isothermal compressibility diverges at equilibrium, indicating phase transition points.

Abstract

We study the corrected entropy due to thermal fluctuation and their effect on the thermodynamics of a conformally dressed black hole in three dimensions. We find that the thermal fluctuation affects the entropy significantly for small black holes. Various corrected thermodynamical variables are also calculated for this black hole. We observe that thermal fluctuation on the thermodynamics of a small conformal black hole has a significant effect. We also analyse the stability of black hole under the effect of thermal fluctuation. Due to thermal fluctuation, instability occurs in the system of small conformal black holes. Isothermal compressibility is also studied for this black hole which diverges for the equilibrium state of the system.