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In this thesis, we apply the AdS/CFT correspondence to space-times associatedwith extensions of General Relativity. We are particularly interested incalculating the transport coefficient, the shear viscosity, associated with theeffective field theory whose dual is a black hole space-time in bulk. Thecorrespondence also allows us to compute thermodynamic quantities, in which theentropy, plays a prominent role when the ratio between the shearviscosity-to-entropy density is taken. This ratio is conjectured to have aminimum value of $1/4{\pi}$, in natural units. The main results presented inthis thesis consist of calculating the ratio for two different cases, and thenapplying the KSS conjecture - which establishes the minimum value for the ratio-, to investigate properties associated with the deformed space-time metrics. Abrief review of General Relativity and Black Holes is presented. The so-calledBrane World formalism is introduced, obtaining the equivalent of Einstein'sequations and Black Hole solutions on the brane, which can be seen asextensions of solutions known in General Relativity. We discuss the formulationof AdS/CFT correspondence, and how to apply it to compute transportcoefficients. Then applying this knowledge to compute transport coefficientsassociated with the solutions constituting an extension of General Relativity.Naturally, throughout the process of developing this work other interestingquestions arise, therefore we include two studies related to thesedevelopments. In one we investigate the computation of transport coefficientswhen we have a fermionic sector in the model. The second is a proposal on howto evaluate the consistency of AdS/CFT correspondence via the calculation ofthe Weyl anomaly.

Transport coefficients associated to black holes on the brane: analysis of the shear viscosity-to-entropy density ratio