We study the quasinormal modes (QNMs) of a charged scalar in the static spherically symmetric black hole background near the event and cosmological horizon. Starting with numerical analysis of the QNMs of black hole in the dRGT massive gravity, the mathematical tool called the asymptotic iteration method (AIM) is used to calculate the quasinormal frequencies. The parameters such as the mass and charge of the black hole, the cosmological constant, the coefficient of the linear term from massive gravity $\gamma$, and the mass of the scalar are varied to study the behavior of the QNMs. We found the tower pattern of the near-horizon quasinormal frequencies from the numerical results by AIM where the real parts depend only on product of the charge of the black hole and the scalar field and the imaginary parts depend only on the surface gravity. To confirm the numerical finding, we analytically determine the exact QNMs of the charged scalar near the horizons of any static spherically symmetric black hole background in the simple universal forms; $\omega =\frac{qQ}{r_h}+i{\kappa }_{h}n$ and $\omega =\frac{qQ}{r_c}+i|{\kappa }_c|n$ where $n$ is a nonpositive integer and ${\kappa }_{h,c}$ is the surface gravity, for the event and cosmological horizon respectively. Extending our analysis, we also compute the four towers of the near-horizon QNMs that can reach the far region. The four kinds of QNMs converge to certain asymptotic values with equally spacing imaginary parts and the real parts proportional to $qQ/r_{h,c}$. These modes do not match with the all-region (WKB) modes of the real background since they originate from the linearly approximated metric.

• Received 2 January 2019

DOI:https://doi.org/10.1103/PhysRevD.99.084002

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society