论文标题
与黑洞相关的传输系数：分析剪切粘度与入口密度比
Transport coefficients associated to black holes on the brane: analysis of the shear viscosity-to-entropy density ratio
论文作者
论文摘要
在本文中，我们将AD/CFT对应关系应用于与一般相对性扩展相关的空间时间。我们特别有兴趣计算传输系数，剪切粘度与有效的场理论相关，该理论是偶数是散装的黑洞时空。该对应关系还允许我们计算热力学量，其中熵在采取剪切粘度与透镜密度之间的比率时起着显着的作用。该比率的最低值为$ 1/4π$，在天然单位中。本文中介绍的主要结果包括计算两种不同情况的比率，然后应用KSS猜想 - 建立比率的最小值，以研究与变形时空指标相关的属性。简要审查了一般相对论和黑洞。引入了所谓的Brane World形式主义，获得了Brane上的Einstein方程和黑洞溶液的等效物，可以看作是在一般相对论中已知的溶液的扩展。我们讨论ADS/CFT对应关系的配方，以及如何将其应用于计算运输系数。然后将此知识应用于计算与构成一般相对性扩展的解决方案相关的传输系数。自然，在制定这项工作的整个过程中，出现了其他有趣的问题，因此我们包括了两项与这些发展有关的研究。在一个模型中，我们研究了运输系数的计算。第二个是关于如何通过WEYL异常计算评估AD/CFT对应关系一致性的建议。
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 $1/4π$, 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.
