Holographic entanglement entropy for relativistic hydrodynamic flows

We study the behaviour of holographic entanglement entropy (HEE) in near equilibrium thermal states which are macroscopically described by conformal relativistic hydrodynamic flows dual to dynamical black brane geometries. We compute HEE for strip-shaped subsystems in boundary dimensions d=2,3,4, which provides us with general qualitative inferences on the interplay between fluid flows and entanglement dynamics. At first, we consider the zeroth order in hydrodynamic derivative expansion, holographically described by stationary boosted black branes. Working non-perturbatively in fluid velocity, we find that, as the fluid velocity approaches its relativistic upper limit, the UV regulated HEE exhibits a divergence, at arbitrary temperature. Also, the holographic mutual information between two relatively close subsystems vanishes at some critical fluid velocity and remains zero beyond it. We then compute HEE in an excited state of the fluid in the presence of a sound mode, considering first order in derivative expansion. As a simplified setup, we first work with non-dissipative dynamics in $d=2$, where the time evolution of HEE is studied in the presence of the sound mode and a propagating pressure pulse. In d= 4, we find that dissipative sound modes produce an additional dynamical UV divergence which is subleading compared to `area law divergence'. No such divergence is observed for dissipative sound mode in d=3.