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

## TL;DR

This paper explores black brane solutions in Lifshitz spacetime within Horndeski gravity, focusing on how the viscosity/entropy ratio behaves at a critical exponent of z=1/2, revealing potential violations of the universal bound.

## Contribution

It provides new black brane solutions in Lifshitz spacetime with a specific critical exponent in Horndeski gravity and analyzes the viscosity/entropy ratio in the dual field theory.

## Key findings

- Viscosity/entropy ratio potentially violates the bound at z=1/2.
- Black brane solutions are constructed for a critical exponent z=1/2.
- The cosmological constant varies with the Lifshitz exponent.

## 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 $\eta/s\geq1/(4\pi)$ at $z=1/2$.