Abstract
In our previous work [18] 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 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 non-extremal 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 WKB approximation.
Highlights
The study of black hole perturbations has a long history dating back to the work of Regge and Wheeler [1] and Vishveshwara [2]
Black holes return to their equilibrium by going through a ringdown phase, whose most dominant stage is characterized by the long lasting damped oscillations dubbed as quasinormal modes (QNMs) [4]
There we investigate the QNM spectrum of the massive, charged scalar field by the Wentzel-Kramers-Brillouin (WKB) method
Summary
The study of black hole perturbations has a long history dating back to the work of Regge and Wheeler [1] and Vishveshwara [2]. In our recent paper [18] we have investigated a model of NC scalar and gauge fields coupled to a classical background of the Reissner-Nordström (RN) black hole This model resulted in a master equation governing the behavior of the scalar perturbations in the presence of a noncommutative structure of spacetime. To overcome the shortcomings of the analytic treatment, in the present work we analyze the same master equation by a well-defined numerical method, the continued fraction method. This method enables us to find solutions for QNM frequencies for a more general set of system parameters. Details of a few cumbersome calculations are given in Appendixes A and B
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