The material presented in this thesis mainly consists of two parts under the umbrella topic of Holographic Duality or the AdS/CFT correspondence.
In Part II we are mainly interested in the properties of energetic quantities, namely, the energy and free energy of Conformal Field Theory (CFT) under de- formations of spacetime geometry in (2+1) dimensions. By using holography together with analytic and numerical techniques, we find many results on monotonic decreasing of the energy/free energy for static solutions of gravitational theory in asymptotically locally Anti-de Sitter (AlAdS) spacetime and correspondingly for a CFT dual in many different scenarios. These results put nontrivial physical bounds on the energy/free energy of holographic CFT in curved spaces.
In Part III, in chapter 6 we study the Gregory-Laflamme (GL) instability of charged black strings in five dimensions. The physical properties of GL unstable mode perturbations and the consequences of the instability are studied in detail. We also solve for numerical solutions of nonuniform phase of charged black strings and obtain a thermodynamic phase structure of charged black strings. In chapter 7, we apply the holographic duality to a black string solution with an extra string charge in the type-IIA supergravity. We utilize the similarity between the properties of charged black strings in five dimensions and our system in type-IIA supergravity to obtain the result on thermodynamics of its holographic dual which is a two- dimensional supersymmetric Yang-Mills theory on a circle in a boosted frame.Open Acces
