Dynamical Evolution Of Electromagnetic Perturbation In The Background Of A Scalar Hairy Black Hole In Horndeski Theory

Quasinormal modes of black holes describe the damped oscillations in the inter-mediate evolution stage of perturbations in the black hole background.It is treated as a characteristic sound of black holes since the oscillation frequencies and damping times contain some characteristic information including black hole parameters.It is an strong evidence of identifying directly the black hole existence in Universe and is expected to be detected in the gravitation wave observations.Moreover,black hole quasinormal modes play an important role in the theoretical study of AdS/CFT correspondence and loop quantum gravity.Thus,it has been a hot topic in black hole physics and the study of black hole quasinormal modes is of great significanceIn this thesis,we adopt the numerical method including WKB approximation to study the dynamical evolution of electromagnetic perturbation in a scalar hairy black hole spacetime,which belongs to Horndeski theory of gravity.And then,we analyze the dependence of quasinormal modes and late-time tail on black hole characteristic parametersIn the first chapter,we introduce briefly quasinormal mode,WKB approxi,mation and Horndeski theory.In the second chapter,we first introduce the scalar hairy black hole solution in the Horndeski theory with a logarithmic cubic term,and then analyze its thermodynamic properties.In the third chapter,we adopt the numerical method to calculate the quasinormal modes and the late-time tail of electromagnetic perturbation in a scalar hairy black hole spacetime,and find that the parameter ? affects not only the event horizon and the asymptotical structure of spacetime at spatial infinity,but also the quasinormal frequency of electromagnetic perturbation.Moreover,due to the existence of solid angle deficit,the parameter? makes the decay of electromagnetic perturbation in the late-time tail stage more rapidly.These imply that the spacetime properties arising from the logarithmic cubic term in the action play important roles in the dynamical evolutions of the electromagnetic perturbation in the background of a scalar hairy black hole.Final-ly,we presented a summary and make some prospects for dynamical evolution in black hole spacetimes.