# Robinson-Trautman spacetimes and gauge/gravity duality

## TL;DR

This paper explores the dynamics of far-from-equilibrium plasmas via gauge/gravity duality using Robinson-Trautman spacetimes, revealing limitations of hydrodynamics and introducing new inhomogeneous plasma flow models.

## Contribution

It demonstrates the applicability limits of hydrodynamics in inhomogeneous plasmas and introduces a new class of holographic plasma flows derived from RT spacetimes.

## Key findings

- Hydrodynamic approximation fails at non-perturbative levels for inhomogeneous data.
- Local rest frame identification is possible perturbatively but not non-perturbatively.
- New inhomogeneous plasma flow models are constructed via coordinate transformations.

## Abstract

We study far-from-equilibrium field theory dynamics using gauge/gravity duality applied to the Robinson-Trautman (RT) class of spacetimes and we present a number of new results. First, we assess the applicability of the hydrodynamic approximation to inhomogeneous plasma dynamics dual to RT spacetimes. We prove that to any order in a late time expansion it is possible to identify variables corresponding to the local energy density and fluid velocity. However, we show using numerical examples that this does not hold at the non-perturbative level; for sufficiently inhomogeneous initial data a local rest frame does not exist. Second, we preset a new class of holographic inhomogeneous plasma flows on the plane. The corresponding spacetimes are not of the RT type but they can be obtained from RT spacetimes with spatially compact boundaries by coordinate transformations which generate Poincar\'e patch-like coordinates with planar boundaries. We demonstrate the application of this procedure using numerical examples.