Gauge/gravity duality and thermalization of a boost-invariant perfect fluid

TL;DR

The paper analyzes how a boost-invariant expanding N=4 SYM fluid thermalizes by studying scalar and metric perturbations in the holographic dual of a black hole moving in the fifth dimension. By deriving and solving the quasinormal mode equations in both static and expanding AdS5 geometries (using Fefferman–Graham coordinates), it reveals a universal, rapidly damped thermalization time and a nontrivial proper-time scaling understood via an adiabatic approximation. The results show that the same QNM spectrum governs both scalar and certain metric perturbations, with a consistent interpretation of the expansion dynamics and potential implications for the short thermalization times observed in heavy-ion collisions. The work suggests an attractor-like behavior toward a perfect fluid regime and outlines directions for incorporating viscosity and perturbations beyond the scalar channel in the expanding background.

Abstract

We derive the equation for the quasi-normal modes corresponding to the scalar excitation of a black hole moving away in the fifth dimension. This geometry is the AdS/CFT dual of a boost-invariant expanding perfect fluid in N=4 SUSY Yang-Mills theory at large proper-time. On the gauge-theory side, the dominant solution of the equation describes the decay back to equilibrium of a scalar excitation of the perfect fluid. Its characteristic proper-time can be interpreted as a thermalization time of the perfect fluid, which is a universal (and numerically small) constant in units of the unique scale of the problem. This may provide a new insight on the short thermalization-time puzzle encountered in heavy-ion collision phenomenology. A nontrivial scaling behaviour in proper-time is obtained which can be interpreted in terms of a slowly varying adiabatic approximation.