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arXiv · 2509.07235

Critical masses and numerical computation of massive scalar quasinormal modes in Schwarzschild black holes

Matheus F. S. Alves·Bruno P. Pônquio·L. G. Medeiros
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Abstract

We present a comprehensive analysis of the quasinormal modes (QNMs) of a massive scalar field in Schwarzschild spacetime using two complementary numerical techniques: the Hill-determinant method and Leaver continued-fraction method. Our study systematically compares the performance, convergence, and consistency of the two approaches across a wide range of field masses and angular momenta. We identify three critical mass thresholds, $m_{\rm lim}$, $m_{\rm max}$, and $m_{zd}$, which govern qualitative changes in the QNM spectrum. In particular, long-lived modes emerge at $m_{zd}$, where the imaginary part of the frequency vanishes and the mode becomes essentially non-decaying. This phenomenon is robust across multipoles and may have important implications for the phenomenology of massive fields around black holes. Our results provide a detailed numerical characterization of massive scalar QNMs and highlight the complementary strengths of the Hill-determinant and continued-fraction methods, paving the way for future studies of rotating or charged black holes and quasi-bound states.

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Matheus F. S. Alves, Bruno P. Pônquio, L. G. Medeiros. 2025-09-08. Critical masses and numerical computation of massive scalar quasinormal modes in Schwarzschild black holes. https://doi.org/10.1103/rjrk-j3jt

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