The dS/CFT Correspondence and Quasinormal Modes of Black Holes

In this thesis we discuss two aspects of quantum gravity and break it up in the following way. In part I, we discuss a scalar field theory living in de Sitter space-time. We may describe the infinite past or future as being boundaries of this space-time and, on these boundaries we construct a field theory. It has been shown by Strominger that there exists a correspondence between the bulk de Sitter space-time and the field theory living in the infinite past [1]. This may be described as a holographic principle, where information in the bulk de Sitter space-time corresponds to information contained in the boundary field theory. We discuss the correspondence in two dimensions where the field theory is represented by a quantum mechanical model with conformal symmetry. We build up the quantum mechanical model and construct its Hamiltonian along with its energy eigenstates. Next, we study the correspondence for a three dimensional asymptotic de Sitter space. By approaching the boundary of the space-time the symmetry is enhanced for the corresponding field theory. These symmetries are generated by charges dictated by Noether’s theorem. We explicitly calculate the generators of these symmetries and show they satisfy the Virasoro algebra with a central extension which helps to create a full picture of the correspondence. In part II, we focus on the ramifications of perturbed black holes in asymptotically anti-de Sitter space-time. By perturbing a black hole, it vibrates in characteristic modes much like the ringing of a bell. These modes are known as quasi-normal modes. We will show that by applying the appropriate boundary conditions, the quasi-normal frequencies are quantized. We calculate the quasi-normal frequencies in four and five dimensions perturbatively for various types of perturbations. Understanding these modes may help in understanding the holographic principle, and can give insight into the intrinsic parameters of the black holes. It is important to understand the characteristic modes and corresponding characteristic frequencies of these black holes in order to hopefully compare to experimental results from future gravitational wave detectors.