Shear viscosity and instability from third order Lovelock gravity

TL;DR

This paper addresses how third-order Lovelock gravity affects the shear viscosity to entropy density ratio and the stability/causality of charged AdS black branes. It computes the transport coefficient via tensor perturbations and the Kubo formula for a RN-AdS black brane with a specific Lovelock coupling, and analyzes causality through the high-frequency graviton propagation and stability via a Schrödinger potential. The key findings are that the eta/s value is $eta/s = (1/(4*pi)) * (1 - (2*lambda/(D-3))*((D-1) - (D-3)*a))$ with $a = q^2 l^2 / r_+^{2D-4}$, independent of lambda^2; no causality violation occurs for the chosen couplings; stability imposes $lambda ≤ 1/4$ in the infinite-D limit with $lambda_{c,min} = 1/4 * ((D-3)(D-4))/((D-1)(D-2))$. These results constrain higher-curvature corrections in AdS/CFT and clarify how third-order Lovelock terms influence transport and the boundary theory's causal structure.

Abstract

We calculate the ratio of shear viscosity to entropy density for charged black branes in third order Lovelock theory. For chargeless black branes, the result turns out to be consistent with the prediction made in $\rm arXiv:0808.3498[\rm hep-th] $. We find that, the third order Lovelock gravity term does not contribute to causality violation unlike the Gauss-Bonnet term. The stability of the black brane again requires the value of the Lovelock coupling constant to be bounded by 1/4 in the infinite dimensionality limit.

Figures (1)

• Figure 1: $c^2_g$ as a function of $u$ and $\lambda$ when we choose $D=7$ and $a=1.4$. The lines correspond to $0.8, 0.6,...,-0.8$, respectively, from left to right.