Black branes in asymptotically Lifshitz spacetime and viscosity/entropy ratios in Horndeski gravity

Abstract

We investigate black brane solutions in asymptotically Lifshitz spacetime in 3+1-dimensional Horndeski gravity, which admit a critical exponent fixed at $z=1/2$. The cosmological constant depends on $z$ as $\Lambda =-(1+2z)/L^2$. We compute the shear viscosity in the 2+1-dimensional dual boundary field theory via holographic correspondence. We investigate the violation of the bound for viscosity to entropy density ratio of $\eta /s\ge 1/(4\pi )$ at $z=1/2$.

7 pages, no figures, 1 table. Version published in EPL