Hydrodynamics in black brane with hyperscaling violation metric background

TL;DR

This paper investigates the shear viscosity to entropy density ratio in a hyperscaling violating black brane background, revealing constraints on the hyperscaling parameter and showing the ratio's independence from it, aligning with known results.

Contribution

It provides new constraints on the hyperscaling violation parameter and demonstrates the ratio's independence from this parameter in a black brane background.

Findings

The ratio ta/s is approximately 1/4pi, consistent with previous literature.

Constraints on ta are   , and ta  independent of .

Results align with QCD perspectives and existing studies.

Abstract

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 $1/4\pi$.