  In this thesis, we apply the AdS/CFT correspondence to space-times associated
with extensions of General Relativity. We are particularly interested in
calculating the transport coefficient, the shear viscosity, associated with the
effective field theory whose dual is a black hole space-time in bulk. The
correspondence also allows us to compute thermodynamic quantities, in which the
entropy, plays a prominent role when the ratio between the shear
viscosity-to-entropy density is taken. This ratio is conjectured to have a
minimum value of $1/4{\pi}$, in natural units. The main results presented in
this thesis consist of calculating the ratio for two different cases, and then
applying the KSS conjecture - which establishes the minimum value for the ratio
-, to investigate properties associated with the deformed space-time metrics. A
brief review of General Relativity and Black Holes is presented. The so-called
Brane World formalism is introduced, obtaining the equivalent of Einstein's
equations and Black Hole solutions on the brane, which can be seen as
extensions of solutions known in General Relativity. We discuss the formulation
of AdS/CFT correspondence, and how to apply it to compute transport
coefficients. Then applying this knowledge to compute transport coefficients
associated with the solutions constituting an extension of General Relativity.
Naturally, throughout the process of developing this work other interesting
questions arise, therefore we include two studies related to these
developments. In one we investigate the computation of transport coefficients
when we have a fermionic sector in the model. The second is a proposal on how
to evaluate the consistency of AdS/CFT correspondence via the calculation of
the Weyl anomaly.
