Einstein-Gauss-Bonnet Black Strings at Large $D$

TL;DR

This paper investigates the stability and dynamics of Einstein-Gauss-Bonnet black strings at large dimensions, deriving effective equations, analyzing instabilities, and exploring non-linear evolution with implications for fluid-like behavior.

Contribution

It derives effective equations for EGB black strings at large D, analyzes their stability, and studies non-linear evolution, revealing how the GB term influences instability and late-time behavior.

Findings

Thin EGB black strings are unstable to Gregory-Laflamme instability.

The GB term can weaken or strengthen the instability depending on its size.

Non-linear evolution leads to stable non-uniform black strings.

Abstract

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.