Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2016-03-22T19:28:11Z No. of bitstreams: 1 MadsonRubemOliveiraSilva_TESE.pdf: 1495464 bytes, checksum: 0d35c3d788f1373d1f29cb97ab81c05a (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2016-03-23T23:12:57Z (GMT) No. of bitstreams: 1 MadsonRubemOliveiraSilva_TESE.pdf: 1495464 bytes, checksum: 0d35c3d788f1373d1f29cb97ab81c05a (MD5) / Made available in DSpace on 2016-03-23T23:12:57Z (GMT). No. of bitstreams: 1 MadsonRubemOliveiraSilva_TESE.pdf: 1495464 bytes, checksum: 0d35c3d788f1373d1f29cb97ab81c05a (MD5) Previous issue date: 2015-05-22 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior - CAPES / A equa??o de Einstein com constante cosmol?gica negativa gera um espa?o-tempo d + 1?dimens?es, que denominamos de espa?o anti de Sitter, AdSd+1, que nos referimos de "bulk". O principio hologr?fico afirma que a gravidade qu?ntica sobre o AdSd+1 ? codificada por uma teoria de contorno, uma CFTd. Por exemplo, uma teoria de cordas IIB sobre uma espa?o-tempo assintoticamente AdS5 ? S 5 ? dual a uma teoria de gauge de super Yang-Mills N = 4 SYM no espa?o-tempo de 4?dimens?es. Outro exemplo ? a rela- ??o entre a equa??o de Einstein no "bulk"e a equa??o hidrodin?mica descreve uma teoria efetiva no contorno, o qual denominamos de fluido/gravita??o. Uma extens?o da dualidadeAdS/CFT foi proposta por Takayanagi que denominou de correspond?ncia AdS/BCFT. O contorno do CFT extende-se para o "bulk"e restringe o AdSd+1. Quando impomos a condi??o de Neumann sobre a extens?o do contorno obtemos uma equa??o de movimento din?mica que determina a forma da extens?o. Da perspectiva da correspond?ncia fluido/gravita??o o tensor energia-momento do fluido residindo no contorno ser? a fonte da geometria do "bulk". Ampliando a proposta de Takayanagi para correspond?ncia fluido/gravita??o estudaremos a consist?ncia do AdS/BCFT a temperatura finita ou equivalentemente a geometria de BH no "bulk". / Einstein?s equations with negative cosmological constant possess the so-called anti de Sitter space, AdSd+1, as one of its solutions. We will later refer to this space as to the "bulk". The holographic principle states that quantum gravity in the AdSd+1 space can be encoded by a d?dimensional quantum field theory on the boundary of AdSd+1 space, invariant under conformal transformations, a CFTd. In the most famous example, the precise statement is the duality of the type IIB string theory in the space AdS5 ? S 5 and the 4?dimensional N = 4 supersymmetric Yang-Mills theory. Another example is provided by a relation between Einstein?s equations in the bulk and hydrodynamic equations describing the effective theory on the boundary, the so-called fluid/gravity correspondence. An extension of the "AdS/CFT duality"for the CFT?s with boundary was proposed by Takayanagi, which was dubbed the AdS/BCFT correspondence. The boundary of a CFT extends to the bulk and restricts a region of the AdSd+1. Neumann conditions imposed on the extension of the boundary yield a dynamic equation that determines the shape of the extension. From the perspective of fluid/gravity correspondence, the shape of the Neumann boundary, and the geometry of the bulk is sourced by the energy-momentum tensor T?? of a fluid residing on this boundary. Clarifying the relation of the Takayanagi?s proposal to the fluid/gravity correspondence, we will study the consistence of the AdS/BCFT with finite temperature CFT?s, or equivalently black hole geometries in the bulk.