Bjorken Flow of Holographic R-Charged Plasmas

Abstract

We numerically investigate the time evolution of several physical observables for the so-called 2 R-Charge Black Hole (2RCBH) model undergoing Bjorken flow. The 2RCBH model corresponds to a top-down holographic construction describing a strongly interacting conformal fluid defined at finite temperature and R-charge density. Taken together with previous findings for the purely thermal $\mathcal{N}=4$ Supersymmetric Yang-Mills (SYM) plasma, and the 1 R-Charge Black Hole (1RCBH) model, our results for the 2RCBH model provide strong numerical evidence for the existence of far-from-equilibrium correlations between the non-equilibrium holographic entropy defined through the area of the apparent horizon of dynamical bulk black holes, and the expectation value of the energy-momentum tensor of the dual boundary quantum field theory. Such correlations are relevant in the pre-hydrodynamic stages of some initial data evolved in time, and seem to hold at least for strongly interacting conformal fluids, be they charged or neutral.

Figures (7)

• Figure 1: Entropy density (a), R-charge density (b), pressure (c), and R-charge susceptibility (d) for the 2RCBH and 1RCBH models in thermodynamic equilibrium.
• Figure 2: Plots for equilibrium dimensionless ratios of thermodynamic observables, both for the 2RCBH and 1RCBH models.
• Figure 3: (a) Normalized pressure anisotropy (solid lines) and the corresponding hydrodynamic Navier-Stokes attractor given by Eqs. \ref{['eq:pressure-anisotropy-EOM']} and \ref{['eq:energyNS']} (dashed lines) --- the gray and red zones indicate violations of the DEC and WEC, respectively; (b) normalized charge density; (c) normalized scalar condensate (solid lines) and the corresponding thermodynamic stable equilibrium result (dashed lines); (d) normalized non-equilibrium entropy density associated to the apparent horizon $\hat{s}_\text{AH}^{4/3}/\hat{\varepsilon}$ (solid lines) and the corresponding thermodynamic stable equilibrium result (dashed lines); (e) radial location of the apparent horizon (solid lines) and event horizon (dashed lines); and (f) non-equilibrium entropy $\hat{S}_H/\mathcal{A}\Lambda^2=\tau \hat{s}_H/\Lambda^2$ calculated from the area of the apparent horizon (solid line) and from the area of the event horizon (dashed lines). The plots make use of each of the four ICs in Table \ref{['tab:parameters']} to compare the time evolution of different initial states of the 1RCBH and 2RCBH plasmas. The results were obtained by calibrating the initial charge density parameter $\rho_0$ such as to produce evolutions equilibrating towards the same approximate value of $\mu/T\approx 1.2$. For all the curves, the initial energy density was fixed using $a_2(\tau_0)=-7.40$.
• Figure 4: (a) Normalized pressure anisotropy (solid lines) and the corresponding hydrodynamic Navier-Stokes attractor given by Eqs. \ref{['eq:pressure-anisotropy-EOM']} and \ref{['eq:energyNS']} (dashed lines) --- the gray and red zones indicate violations of the DEC and WEC, respectively; (b) normalized charge density; (c) normalized scalar condensate (solid lines) and the corresponding thermodynamic stable equilibrium result (dashed lines); (d) normalized non-equilibrium entropy density associated to the apparent horizon $\hat{s}_\text{AH}^{4/3}/\hat{\varepsilon}$ (solid lines) and the corresponding thermodynamic stable equilibrium result (dashed lines); (e) radial location of the apparent horizon (solid lines) and event horizon (dashed lines); and (f) non-equilibrium entropy $\hat{S}_H/\mathcal{A}\Lambda^2=\tau \hat{s}_H/\Lambda^2$ calculated from the area of the apparent horizon (solid line) and from the area of the event horizon (dashed lines). The results were obtained by varying the initial charge density parameter $\rho_0$, while keeping $B_s$ and $\phi_s$ fixed according to the IC#01 in Table \ref{['tab:parameters']}, with $a_2(\tau_0)=-6.6667$.
• Figure 5: (a) Normalized pressure anisotropy (solid lines) and the corresponding hydrodynamic Navier-Stokes attractor given by Eqs. \ref{['eq:pressure-anisotropy-EOM']} and \ref{['eq:energyNS']} (dashed lines) --- the gray and red zones indicate violations of the DEC and WEC, respectively; (b) normalized charge density; (c) normalized scalar condensate (solid lines) and the corresponding thermodynamic stable equilibrium result (dashed lines); (d) normalized non-equilibrium entropy density associated to the apparent horizon $\hat{s}_\text{AH}^{4/3}/\hat{\varepsilon}$ (solid lines) and the corresponding thermodynamic stable equilibrium result (dashed lines); (e) radial location of the apparent horizon (solid lines) and event horizon (dashed lines); and (f) non-equilibrium entropy $\hat{S}_H/\mathcal{A}\Lambda^2=\tau \hat{s}_H/\Lambda^2$ calculated from the area of the apparent horizon (solid line) and from the area of the event horizon (dashed lines). The results were obtained by varying the initial charge density parameter $\rho_0$, while keeping $B_s$ and $\phi_s$ fixed according to the IC#02 in Table \ref{['tab:parameters']}, with $a_2(\tau_0)=-6.6667$.