Metastable Black Saturns

TL;DR

This paper investigates the thermodynamic phases and metastability of black Saturns, revealing a narrow angular momentum window where metastable configurations exist, suggesting a link between thermal and classical stability.

Contribution

It numerically identifies metastable black Saturn phases and links their stability range to classical stability, extending understanding of black hole thermodynamics.

Findings

Metastability occurs in a narrow angular momentum window 0.92457<j<0.92463.

Most balanced Saturns are not metastable when entropy Hessian is negative definite.

Thermal stability may be connected to classical stability, similar to Gubser-Mitra conjecture.

Abstract

Black Saturns have multiple horizons and so offer a testing ground for the ideas of black hole thermodynamics. In this note, we numerically scan for phases that are in equilibrium by extremizing total entropy in the 2-dimensional moduli space of stationary, singly rotating black Saturns with fixed total mass and angular momentum. On top of the known T_H=T_R, Omega_H=Omega_R configurations, we find phases that do not balance the temperature and angular velocity of the ring and the hole. But these (and most of the balanced Saturns) go away when we demand that the system is metastable, by imposing that the Hessian of the entropy is negative definite. Metastablity occurs when the dimensionless total angular momentum lies in a narrow window 0.92457<j<0.92463 of the thin ring branch. This is consistent with the expected range of classical stability of black Saturns and therefore may imply that thermal stability is tied to classical stability, in analogy with Gubser-Mitra in the translationally-invariant case. We also comment on the possibility of constructing plasma configurations that are dual to black Saturns in AdS.