Abstract
In this study, analytical calculations are performed to assess the quasinormal modes (qnm) of the perturbed electromagnetic potential within the a four-dimensional spacetime of the Reissner-Nordström (RN) anti-de Sitter (AdS) black holes which are dressed with scalar hair. The black holes serve as the solutions for the Einstein-Maxwell theory under a negative cosmological constant and conformally-coupled real self-interacting scalar field. When the strength of the scalar field is suitable, phase transition of the black holes occurs to create a new form of MTZ black holes. The electromagnetic field can then be perturbed and the qnm and their frequencies calculated in order to meet the boundary conditions both at the horizon and at the far distant region from the new MTZ black hole. In order to address a simplified version of this problem, this study investigates the case whereby the mass of the MTZ black hole is significantly less than the AdS radius.
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