Hydrodynamics in black brane with hyperscaling violation metric background

Understand

In this paper we consider a metric with hyperscaling violation on black brane background.

• In this background we calculate the ratio of shear viscosity to entropy density with hydrodynamics information.
• The calculation of this quantity lead us to constraint $\theta$ as $3\leq\theta<4$, and $\theta\leq0$.
• In that case we show that the quantity of $\frac{\eta}{s}$ not dependent to hyperscaling violation parameter $\theta.$ Our results about ratio of shear viscosity to entropy density in direct of $QCD$ point of view agree with other works in literature as $1/4\pi$.