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.
Highlights
Black-hole solutions of the Einstein equations in general relativity (GR) are useful tools to investigate the spacetime structure and quantum effects in any possible theory of gravity
We consider the lower bound for the shear viscosity-to-entropy density ratio, obtained from the fluid/ gravity correspondence, in order to constrain the postNewtonian parameter of brane-world metrics
One of the most remarkable predictions of the antide Sitter (AdS)/CFT and fluid/gravity correspondence is the ratio of the shear viscosity-to-entropy density, which is universal for a large class of strongly coupled isotropic plasmas [9]
Summary
Black-hole solutions of the Einstein equations in general relativity (GR) are useful tools to investigate the spacetime structure and quantum effects in any possible theory of gravity. In the long-wavelength limit, the fluid/gravity correspondence has been recently proposed as a framework related to the AdS/CFT correspondence [14,15,16], mapping black holes in asymptotically AdS spacetimes to the fluid dynamics of a strongly coupled boundary field theory. One of the most remarkable predictions of the AdS/CFT and fluid/gravity correspondence is the ratio of the shear viscosity-to-entropy density, which is universal for a large class of strongly coupled (gauge theory) isotropic plasmas [9]. The hydrodynamic features of the horizon of a black string can be identified with the hydrodynamic behaviour of a dual theory For such QFTs, the ratio of the shear viscosity η to entropy density s is bounded by the universal value [17].
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