Inhomogeneous holographic thermalization

TL;DR

This paper models inhomogeneous holographic thermalization in strongly coupled conformal field theories, deriving analytic results that connect early free streaming behavior to viscous hydrodynamics, with implications for heavy ion collision experiments.

Contribution

It extends previous homogeneous models by including inhomogeneities and provides analytic solutions in a long wavelength expansion, bridging free streaming and hydrodynamics.

Findings

Early-time evolution matches free streaming model.

Stress tensor approaches second-order viscous hydrodynamics.

Analytic results valid in a long wavelength regime.

Abstract

The sudden injection of energy in a strongly coupled conformal field theory and its subsequent thermalization can be holographically modeled by a shell falling into anti-de Sitter space and forming a black brane. For a homogeneous shell, Bhattacharyya and Minwalla were able to study this process analytically using a weak field approximation. Motivated by event-by-event fluctuations in heavy ion collisions, we include inhomogeneities in this model, obtaining analytic results in a long wavelength expansion. In the early-time window in which our approximations can be trusted, the resulting evolution matches well with that of a simple free streaming model. Near the end of this time window, we find that the stress tensor approaches that of second-order viscous hydrodynamics. We comment on possible lessons for heavy ion phenomenology.