Black hole-black string phase transitions from hydrodynamics

TL;DR

This paper explores phase transitions between different plasma states and their dual black objects in AdS space, using fluid dynamics and holography to predict and analyze their thermodynamic behaviors and instabilities.

Contribution

It introduces a novel application of fluid/gravity correspondence to study black hole-black string phase transitions and predicts phase diagrams in AdS space.

Findings

Phase diagrams of AdS black objects resemble those in Kaluza-Klein systems.

Critical dimension for string transition matches Kaluza-Klein results.

Holographic approach links Rayleigh-Plateau and Gregory-Laflamme instabilities.

Abstract

We discuss the phase transitions between three states of a plasma fluid (plasma ball, uniform plasma tube, and non-uniform plasma tube), which are dual to the corresponding finite energy black objects (black hole, uniform black string, and non-uniform black string) localized in an asymptotically locally AdS space. Adopting the equation of state for the fluid obtained by the Scherk-Schwarz compactification of a conformal field theory, we obtain axisymmetric static equilibrium states of the plasma fluid and draw the phase diagrams with their thermodynamical quantities. By use of the fluid/gravity correspondence, we predict the phase diagrams of the AdS black holes and strings on the gravity side. The thermodynamic phase diagrams of the AdS black holes and strings show many similarities to those of the black hole-black string system in a Kaluza-Klein vacuum. For instance, the critical dimension for the smooth transition from the uniform to non-uniform strings is the same as that in the Kaluza-Klein vacuum in the canonical ensemble. The analysis in this paper may provide a holographic understanding of the relation between the Rayleigh-Plateau and Gregory-Laflamme instabilities via the fluid/gravity correspondence.