Noncommutative scalar field in the nonextremal Reissner-Nordström background: Quasinormal mode spectrum

Abstract

In our previous work [M. D. \ifmmode \acute{C}\else \'{C}\fi{}iri\ifmmode \acute{c}\else \'{c}\fi{} et al., Classical Quantum Gravity 35, 175005 (2018)] we constructed a model of a noncommutative, charged, and massive scalar field based on the angular twist. Then we used this model to analyze the motion of the scalar field in the Reissner-Nordstr\"om black hole background. In particular, we determined the quasinormal mode (QNM) spectrum analytically in the near-extremal limit. To broaden our analysis, in this paper we apply a well-defined numerical method, the continued fraction method, and calculate the QNM spectrum for a nonextremal Reissner-Nordstr\"om black hole. To check the validity of our analytic calculations, we compare results of the continued fraction method in the near extremal limit with the analytic results obtained in the previous paper. We find that the results are in good agreement. For completeness, we also study the QNM spectrum in the Wentzel-Kramers-Brillouin approximation.