# Noncommutative scalar field in the non-extremal Reissner-Nordstr\"om background: QNM spectrum

## TL;DR

This paper extends previous analytical work by numerically calculating the quasinormal mode spectrum of a noncommutative scalar field in non-extremal Reissner-Nordström black holes, confirming the analytic results and exploring the spectrum with WKB approximation.

## Contribution

It applies the continued fraction numerical method to compute QNM spectra for non-extremal black holes, validating previous analytical results and analyzing the spectrum with WKB approximation.

## Key findings

- Numerical QNM spectra agree with analytical results in the near-extremal limit.
- WKB approximation provides additional insights into the QNM spectrum.
- The study broadens understanding of noncommutative scalar fields in black hole backgrounds.

## 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.