Spherically expanding matter in AdS/CFT

TL;DR

This work constructs an exact 5d AdS gravity solution with O(3) symmetry to holographically model a spherically expanding, thermally equilibrated 4d gauge theory on a flat FRW boundary with scale factor $r(t)$. Through holographic renormalization and horizon thermodynamics, the boundary energy density $psilon(t)$ splits into a temperature-dependent part $psilon_0(t)\,/r^4$ and curvature-induced corrections $elta psilon(t)\,pprox r'^4/r^4$, while the boundary pressure satisfies a conformal relation and the entropy density is set by the dynamical horizon $s(t)$. Regularity of the bulk curvature invariant ${al R}_{MNPQ}^2$ at the horizon selects the adiabatic power $psilon o psilon_0/t^4$, linking late-time boundary dynamics to horizon geometry and yielding a consistent equation of state with a temperature related to the horizon via $T_H=1/(mp z_0)$. The analysis demonstrates how a gravity dual can encode time-dependent expansion, horizon dynamics, and quantum corrections in a controllable AdS/CFT setup, providing a framework for probing time-dependent transport in strongly coupled plasmas.

Abstract

We discuss an exact time dependent O(3) symmetric solution with a horizon of the 5d AdS classical gravity equations searching for a 4d boundary theory which would correspond to expanding gauge theory matter. The boundary energy-momentum tensor and entropy density are computed. The boundary metric is the flat Friedmann one and any time dependence on the boundary is incompatible with Minkowski metric. However, at large times when curvature effects are negligible, perfect fluid behavior arises in a natural way.