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We study the quasinormal modes (QNMs) of charged scalar in the staticspherically symmetric black hole background near the event and cosmologicalhorizon. Starting with numerical analysis of the QNMs of black hole in the dRGTmassive gravity, the mathematical tool called the Asymptotic IterationMethod~(AIM) is used to calculate the quasinormal frequencies. The parameterssuch as the mass and charge of the black hole, the cosmological constant, thecoefficient of the linear term from massive gravity $\gamma$, and the mass ofthe scalar are varied to study the behavior of the QNMs. We found the towerpattern of the near-horizon quasinormal frequencies from the numerical resultsby AIM where the real parts depend only on product of the charge of the blackhole and the scalar field and the imaginary parts depend only on the surfacegravity. To confirm the numerical finding, we analytically determine the exactQNMs of the charged scalar near the horizons of any static sphericallysymmetric black hole background in the simple universal forms; $\omega =\displaystyle{\frac{qQ}{r_h}} + i \kappa_h n$ and $\omega =\displaystyle{\frac{qQ}{r_c}} + i |\kappa_c| n$ where $n$ is a non-positiveinteger and $\kappa_{h,c}$ is the surface gravity, for the event andcosmological horizon respectively. Extending our analysis, we also compute thefour towers of the near-horizon QNMs that can reach the far region. The fourkinds of QNMs converge to certain asymptotic values with equally spacingimaginary parts and the real parts proportional to $qQ/r_{h,c}$. These modes donot match with the all-region~(WKB) modes of the real background since they areoriginated from the linearly approximated metric.

Near-horizon quasinormal modes of charged scalar around a general spherically symmetric black hole