Stability of linear dilaton black holes at the Hagedorn temperature

TL;DR

This paper investigates the thermodynamic stability and fluctuation dynamics of a linear dilaton black hole at the Hagedorn temperature, revealing marginal stability and clarifying the nature of certain singularities.

Contribution

It provides a detailed analysis of the thermodynamics and fluctuations of a specific black hole model, showing its marginal stability at the Hagedorn temperature and clarifying the physical significance of correlator singularities.

Findings

Black hole is in a Hagedorn phase with marginal stability

Speed of sound in the dual theory vanishes

No evident supergravity instabilities

Abstract

We study the thermodynamics and the small fluctuations of a linear dilaton black hole, in an S-dual version of the near-horizon limit of type IIB NS5 branes. The thermodynamical analysis shows that the black hole is in a Hagedorn phase, with marginal stability. The dynamical analysis confirms that the speed of sound of the dual theory vanishes and that there are no evident instabilities at the level of supergravity. We clarify the physical meaning of some singularities of the retarded correlator that were thought to lead to instabilities.