EUP-corrected thermodynamics of BTZ black hole

TL;DR

This paper explores how the extended uncertainty principle (EUP) modifies the thermodynamic properties of BTZ black holes in (2+1)-dimensional (A)dS space, revealing new behaviors like critical horizons and stability conditions.

Contribution

It introduces EUP corrections to BTZ black hole thermodynamics and analyzes their effects in (A)dS space, highlighting differences from classical thermodynamics.

Findings

EUP-corrected thermodynamic functions show distinct behaviors in (A)dS space.

A critical horizon with non-zero minimum pressure exists in AdS space.

Black hole stability is affected by pressure, with collapse occurring after a certain horizon.

Abstract

In this manuscript, we investigate the influence of the extended uncertainty principle (EUP) on the thermodynamics of a charged rotating Ba\~{n}ados, Teitelboim and Zanelli (BTZ) black hole in (2+1)-dimensional anti-de Sitter (AdS) and de Sitter (dS) space-time, respectively. We find that EUP-corrected Hawking temperature, entropy, volume, Gibbs free energy, pressure, and heat capacity functions have different characteristic behaviors in (A)dS space-time. During the detailed analysis, we obtain a critical horizon in the AdS space-time where the pressure has a non-zero minimum value. However, in the dS space-time, we cannot achieve such a minimum pressure value. Instead, there is a "cut point" where the pressure becomes zero. We show that after that horizon value the black hole becomes unstable, with negative pressure which leads to the collapse of the black hole.