Black Branes in a Box: Hydrodynamics, Stability, and Criticality

TL;DR

This paper investigates how confining black branes in a finite cavity affects their hydrodynamic stability, revealing a critical cavity size where the Gregory-Laflamme instability is suppressed and analyzing related thermodynamic and transport properties.

Contribution

It introduces a detailed effective hydrodynamic model for black branes in a finite cavity, showing how boundary conditions influence stability and critical behavior, including viscosity and sound speed.

Findings

Black branes become stable below a critical cavity radius.

The squared speed of sound increases with cavity size.

Viscosities remain constant with cavity radius.

Abstract

We study the effective hydrodynamics of neutral black branes enclosed in a finite cylindrical cavity with Dirichlet boundary conditions. We focus on how the Gregory-Laflamme instability changes as we vary the cavity radius R. Fixing the metric at the cavity wall increases the rigidity of the black brane by hindering gradients of the redshift on the wall. In the effective fluid, this is reflected in the growth of the squared speed of sound. As a consequence, when the cavity is smaller than a critical radius the black brane becomes dynamically stable. The correlation with the change in thermodynamic stability is transparent in our approach. We compute the bulk and shear viscosities of the black brane and find that they do not run with R. We find mean-field theory critical exponents near the critical point.