The Horizon Area Spectrum And Entropy Spectrum In Gauss-Bonnet De-Sitter Space-time

In this thesis, we study the horizon area spectrum and entropy spectrum in Gauss-Bonnet de-Sitter space-time. With the new physical interpretation of quasinormal modes proposed by Maggiore, the determination of the area spec-trum and entropy spectrum of black holes have been investigated recently. Tak-ing into account the modified Hod’s treatment as well as Kunstatter’s method, results show that the area and entropy spectra for black holes in Einstein gravity are evenly spaced with the spacings△A=8πh and△S=2π. On the other hand, for higher derivative gravity, the studies show that the area spectrum for a5-dimensional Gauss-Bonnet black hole is not equally spaced, but the quantum entropy spectra is still equidistant. In this thesis, by utilizing the methods of Hod, Kunstatter, and Maggiore, we study area and entropy spectrum of Gauss-Bonnet gravity in de Sitter space-times for both cosmological horizon and black hole event horizon.The thesis is consists of8chapters. In Chapter1and2, we give a brief in-troduction of black holes as well as their geometric properties, thermodynamic property and Hawking radiation. In Chapter3, we give a brief introduction of black hole event horizon entropy and area quantization. In Chapter4, we review the static spherically symmetric solutions of GB dS gravity and its ther-modynamical properties. In Chapter5, we first find the Quasinormal frequen-cies of massive field perturbation in empty dS GB space-time and study the area/entropy spectrum for the cosmological horizon and show that the calcu-lated spectrum behaves different from previous works, the entropy spectrum is equally spaced and does not depend on the cosmological constant A and Gauss-Bonnet term α, the spacing is△S=4π, and the area spectrum is not equally spaced, the spacing is△A=16πh+g(An,n+1), we find that a correction term9(An,n+1) is added in the the area spectrum. In Chapter6, we consider the area/entropy quantization for near-extreme solutions, the entropy spectrum is also equally spaced and the area spectrum is not equally spaced, but the values are not the same, the spacing of entropy spectrum is△S=2π, and the spacing of area spectrum is△A=8πh+g(An,n+1). In Chapter7, we attempt to find area/entropy quantum for non-extremal black holes by using quasinormal fre-quency method and also make some discussion on other possible approaches. In Chapter8, contains the summary of the results and their discussion.