From static to evolving geometries -- R-charged hydrodynamics from supergravity

TL;DR

The work addresses the time-dependent, strongly coupled plasma dynamics with conserved R-charge using the AdS/CFT correspondence. It shows that asymptotic evolving boost-invariant geometries can be generated from the static charged black hole by replacing the radial coordinate with a scaling variable, yielding charge density that scales as $\rho(\tau) \propto 1/\tau$ and energy density $\varepsilon(\tau) \propto \tau^{-4/3}$. Thermodynamics of the evolving state yields $s \propto 1/\tau$, $T \propto \tau^{-1/3}$, and an equation of state with $\varepsilon(s,\rho)=\frac{3 s^{4/3}}{2 (2\pi N_c)^{2/3}}\left(1+\frac{4\pi^2 \rho^2}{3 s^2}\right)$, subject to stability bounds; turning on a dilaton shows that electric and magnetic modes equilibrate rapidly and do not survive to late times. The findings reinforce that the late-time dynamics of a strongly coupled plasma with R-charge is effectively perfect-fluid like, while providing a concrete holographic mechanism for the rapid equilibration of electromagnetic modes.

Abstract

We show that one can obtain asymptotic evolving boost-invariant geometries in a simple manner from the corresponding static solutions. We exhibit the procedure in the case of a supergravity dual of R-charged hydrodynamics by turning on a supergravity gauge field and analyze the relevant thermodynamics. Finally we consider turning on the dilaton and show that electric and magnetic modes in the plasma equilibrate before reaching asymptotic proper times.