Shear viscosity, instability and the upper bound of the Gauss-Bonnet coupling constant

TL;DR

The paper addresses how Gauss-Bonnet corrections and charge affect the holographic shear viscosity to entropy density in $D$-dimensional AdS black branes. It derives the exact $\eta/s$ relation $\eta/s = \frac{1}{4\pi} \left(1 - \frac{2\lambda}{D-3} \big[(D-1) - (D-3)a\big] \right)$ with $a = \frac{q^2 l^2}{r_+^{2D-4}}$ and shows that extremality ($a=\frac{D-1}{D-3}$) removes Gauss-Bonnet corrections. Through causality (via the effective graviton speed) and stability (via the Schrödinger potential for tensor modes) analyses, it establishes dimension-dependent bounds on $\lambda$ that converge to $\frac{1}{4}$ as $D\to\infty$, with a minimal bound $\lambda_{\rm c,min} = \frac{1}{4} \frac{(D-3)(D-4)}{(D-1)(D-2)}$ in the extremal limit. The results imply higher dimensions stabilize tensor perturbations and that the upper bound on Gauss-Bonnet coupling is consistently $\lambda \le \frac{1}{4}$ in the large-$D$ limit, reinforcing the connection between causality, stability, and holographic hydrodynamics in higher-derivative gravity.

Abstract

We compute the dimensionality dependence of $η/s$ for charged black branes with Gauss-Bonnet correction. We find that both causality and stability constrain the value of Gauss-Bonnet coupling constant to be bounded by 1/4 in the infinite dimensionality limit. We further show that higher dimensionality stabilize the gravitational perturbation. The stabilization of the perturbation in higher dimensional space-time is a straightforward consequence of the Gauss-Bonnet coupling constant bound.

Figures (3)

• Figure 1: The minimal value of $\lambda$ constrained by causality. The upper bound of $\lambda$ is $1/4$.
• Figure 2: Schrodinger potential V(u) as a function of $u$ ($u=\frac{1}{z}$) and $D$ for $\lambda=0.24$ and $a=\frac{D-1}{D-3}$.
• Figure 3: The minimal value of $\lambda$ constrained by instability in the limit $a\rightarrow \frac{D-1}{D-3}$. The figure shows that $\lambda_c$ is bounded by $0.25$