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

TL;DR

This thesis uses the AdS/CFT correspondence to calculate the shear viscosity-to-entropy density ratio for black holes in brane-world models, testing the KSS conjecture and exploring extensions of General Relativity.

Contribution

It provides new calculations of the viscosity-to-entropy ratio for brane-world black holes and investigates the effects of space-time deformations on this ratio.

Findings

The ratio is consistent with the KSS bound of 1/4π in studied models.

Deformed metrics influence the shear viscosity-to-entropy density ratio.

Additional studies include fermionic sectors and Weyl anomaly evaluations.

Abstract

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.