标题： 膜上黑洞相关的输运系数：剪切粘度与熵密度比值的分析 显示英文标题

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

摘要： 在本论文中，我们将AdS/CFT对应关系应用于与广义相对论扩展相关的时空。 我们特别感兴趣的是计算与有效场论相关的输运系数，该有效场论的对偶是体中的黑洞时空。 该对应关系还允许我们计算热力学量，在这些量中，当考虑剪切粘度与熵密度的比值时，熵起着显著的作用。 这个比值被猜想在自然单位下有一个最小值$1/4{\pi}$。 本论文的主要结果包括计算两种不同情况下的比值，然后应用KSS猜想——该猜想确立了比值的最小值 -， 以研究与变形时空度规相关的特点。 简要回顾了广义相对论和黑洞。 所谓的膜世界形式主义被引入，得到了膜上爱因斯坦方程和黑洞解的等效形式，这些可以被视为广义相对论中已知解的扩展。 我们讨论了AdS/CFT对应的表述，以及如何应用它来计算输运系数。 然后将这种知识应用于计算与构成广义相对论扩展的解相关的输运系数。 自然地，在开展这项工作的过程中会出现其他有趣的问题，因此我们包含了两个与这些发展相关的研究。 其中一个研究了在模型中存在费米子部分时输运系数的计算。 第二个是关于如何通过计算Weyl反常来评估AdS/CFT对应的合理性的提议。 显示英文摘要

摘要： 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.