The Study Of Quasinormal Modes For The Maxwell Field On Schwarzschild-AdS Black Holes With A Global Monopole

Black hole perturbation theory has attracted a lot of attention for quite a long time.Based on the black hole perturbation theory,the evolution of perturbing fields may be divided into three stages: initial outburst of radiation,damping proper oscillations(also known as quasinormal modes)and power-law or exponential late-time tails.In this thesis,we focus on the second stage,i.e.quasinormal modes(QNMs).To be specific,we study the Maxwell QNMs around a global monopole Schwarzschild-anti-de Sitter black holes with Robin type vanishing energy flux boundary conditions.We first formulate the Maxwell equations both in the Regge-Wheeler-Zerilli and in the Teukolsky formalisms and derive,based on the vanishing energy flux principle,two boundary conditions in each formalism.The Maxwell equations are then solved analytically in pure anti-de Sitter spacetimes with a global monopole,and two different normal modes are obtained.In the small black hole and low frequency approximations,the Maxwell QNMs are solved perturbatively on top of normal modes by using an asymptotic matching method,while beyond the aforementioned approximation,the Maxwell quasinormal modes are obtained numerically by using a matrix method.We analyze the Maxwell QNMs by varying various parameters,and in particular,the monopole parameter.We show explicitly,through calculating quasinormal frequencies with both boundary conditions,that the global monopole produces the repulsive force.