Fluid/gravity correspondence and the CFM black brane solutions

TL;DR

This paper explores how the fluid/gravity correspondence can constrain brane-world metrics, specifically the CFM black brane solutions, by analyzing the shear viscosity-to-entropy density ratio and its relation to experimental bounds on post-Newtonian parameters.

Contribution

It demonstrates that including higher order hydrodynamic terms aligns CFM black branes with experimental bounds, supporting the physical relevance of the viscosity-to-entropy ratio lower bound.

Findings

CFM black branes are effectively Schwarzschild black branes.

Higher order hydrodynamic terms improve agreement with experimental bounds.

Fluid/gravity correspondence constrains brane-world metric parameters.

Abstract

We consider the lower bound for the shear viscosity-to-entropy density ratio, obtained from the fluid/gravity correspondence, in order to constrain the post-Newtonian parameter of brane-world metrics. In particular, we analyse the Casadio-Fabbri-Mazzacurati (CFM) effective solutions for the gravity side of the correspondence and argue that including higher order terms in the hydrodynamic expansion can lead to a full agreement with the experimental bounds, for the Eddington-Robertson-Schiff post-Newtonian parameter in the CFM metrics. This lends further support to the physical relevance of the viscosity-to-entropy ratio lower bound and fluid/gravity correspondence. Hence we show that CFM black branes are, effectively, Schwarzschild black branes.