Perturbation of large anti-desitter black holes and AdS/CFT correspondence

Abstract

As the main goal of this thesis, the canonical form of the perturbation metric of anti-de Sitter black holes in four dimensions is derived by choosing the Regge-Wheeler gauge in the standard Schwarzschild coordinates (t, r, θ, φ). By assuming the perturbations to be small, the differential equations governing the perturbations are obtained from the equations δRμν(h) = 0. Then, by taking the limit of m >> R where R is the radius of AdS space, the perturbation metric and field equations of large AdS black holes are found. Finally, under the shadow of AdS/CFT correspondence, these perturbations can be compared to their corresponding three-dimensional theory of fluid dynamics on the dual space, R × S². Furthermore, by using the definitions of stress-energy tensor and its perturbation, we can find energy density, pressure and shear viscosity which are the quantities we need to describe the behavior of the fluid on the boundary of the AdS space.