Einstein-Gauss-Bonnet Black Strings at Large DD

We study the black string solutions in the Einstein-Gauss-Bonnet(EGB) theory at large $D$. By using the $1/D$ expansion in the near horizon region we derive the effective equations that describe the dynamics of the EGB black strings. The uniform and non-uniform black strings are obtained as the static solutions of the effective equations. From the perturbation analysis of the effective equations, we find that thin EGB black strings suffer from the Gregory-Laflamme instablity and the GB term weakens the instability when the GB coefficient is small, however, when the GB coefficient is large the GB term enhances the instability. Furthermore, we numerically solve the effective equations to study the non-linear instability. It turns out that the thin black strings are unstable to developing inhomogeneities along their length, and at late times they asymptote to the stable non-uniform black strings. The behavior is qualitatively similar to the case in the Einstein gravity. Compared with the black string instability in the Einstein gravity at large D, when the GB coefficient is small the time needed to reach to final state increases, but when the GB coefficient is large the time to reach to final state decreases. Starting from the point of view in which the effective equations can be interpreted as the equations for the dynamical fluid, we evaluate the transport coefficients and find that the ratio of the shear viscosity and the entropy density agrees with that obtained previously in the membrane paradigm after taking the large $D$ limit.Comment: 22 pages, 8 figures, some errors corrected, references adde

Holographic Turbulence in Einstein-Gauss-Bonnet Gravity at Large DD

We study the holographic hydrodynamics in the Einstein-Gauss-Bonnet(EGB) gravity in the framework of the large $D$ expansion. We find that the large $D$ EGB equations can be interpreted as the hydrodynamic equations describing the conformal fluid. These fluid equations are truncated at the second order of the derivative expansion, similar to the Einstein gravity at large $D$. From the analysis of the fluid flows, we find that the fluid equations can be taken as a variant of the compressible version of the non-relativistic Navier-Stokes equations. Particularly, in the limit of small Mach number, these equations could be cast into the form of the incompressible Navier-Stokes equations with redefined Reynolds number and Mach number. By using numerical simulation, we find that the EGB holographic turbulence shares similar qualitative feature as the turbulence from the Einstein gravity, despite the presence of two extra terms in the equations of motion. We analyze the effect of the GB term on the holographic turbulence in detail.Comment: 30 pages, 11 figure