Note on the thermodynamic stability of a black ring at quantum scales

TL;DR

This paper investigates the thermodynamic stability of quantum-scale black rings in AdS space, revealing stability conditions, the absence of critical points, and the occurrence of Hawking-Page transitions.

Contribution

It provides a novel analysis of black ring thermodynamics at quantum scales, highlighting stability limits and phase transitions in AdS space.

Findings

Small black rings are thermodynamically stable due to quantum effects.

Black rings are less stable than thermal AdS.

Hawking-Page transition to radiation occurs without a critical point.

Abstract

In this paper, the thermodynamic properties of a thin black ring in AdS space-time is explored when the size of the ring is comparable to quantum scales. The angular momentum to mass ratio of this system has an upper limit, which is the cosmological radius of the black ring. It is found that the small black ring will be thermodynamically stable due to the effects introduced by thermal fluctuations. However, we find that the black ring is less stable than thermal AdS. Thermodynamic analysis indicates that there is no critical point, but there is Hawking-Page transition to radiation, which is confirmed by the Gibbs free energy analysis.