# Phase Transitions, Inhomogeneous Horizons and Second-Order Hydrodynamics

## TL;DR

This paper uses holography to analyze the evolution of spinodal instabilities in a strongly-coupled gauge theory, demonstrating that second-order hydrodynamics accurately describes the dynamics and final inhomogeneous states.

## Contribution

It introduces a holographic approach to study inhomogeneous black brane instabilities and derives a nonlinear differential equation for final states within second-order hydrodynamics.

## Key findings

- Second-order hydrodynamics accurately describes the instability evolution.
- Final inhomogeneous states can be derived from a single nonlinear differential equation.
- The dual gravity configurations exhibit Gregory-Laflamme instability.

## Abstract

We use holography to study the spinodal instability of a four-dimensional, strongly-coupled gauge theory with a first-order thermal phase transition. We place the theory on a cylinder in a set of homogeneous, unstable initial states. The dual gravity configurations are black branes afflicted by a Gregory-Laflamme instability. We numerically evolve Einstein's equations to follow the instability until the system settles down to a stationary, inhomogeneous black brane. The dual gauge theory states have constant temperature but non-constant energy density. We show that the time evolution of the instability and the final states are accurately described by second-order hydrodynamics. In the static limit, the latter reduces to a single, second-order, non-linear differential equation from which the inhomogeneous final states can be derived.