Waveform stability for the piecewise step approximation of Regge-Wheeler potential
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908922588168192 |
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| author | Wu, Liang-Bi Xie, Libo Zhou, Yu-Sen Guo, Zong-Kuan Cai, Rong-Gen |
| author_facet | Wu, Liang-Bi Xie, Libo Zhou, Yu-Sen Guo, Zong-Kuan Cai, Rong-Gen |
| contents | By interpreting the difference between the original Regge-Wheeler potential and its piecewise step approximation as perturbative effects induced by the external environment of the black hole, we investigate the stability of Schwarzschild black hole time-domain waveforms. In this work, we employ the Green's function method under the assumption of an observer at spatial infinity to obtain the waveform. For two cases in which the initial Gauss bump near the event horizon or at spatial infinity, we derive analytic expressions for the corresponding waveforms. Our results demonstrate that the waveform is indeed insensitive to tiny modifications of the effective potential, thereby confirming its stability. More importantly, we find that broader initial bumps imprint the influence of small environmental modifications more clearly on the waveform, which may provide theoretical guidance for probing the exterior environment of black holes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Waveform stability for the piecewise step approximation of Regge-Wheeler potential Wu, Liang-Bi Xie, Libo Zhou, Yu-Sen Guo, Zong-Kuan Cai, Rong-Gen General Relativity and Quantum Cosmology By interpreting the difference between the original Regge-Wheeler potential and its piecewise step approximation as perturbative effects induced by the external environment of the black hole, we investigate the stability of Schwarzschild black hole time-domain waveforms. In this work, we employ the Green's function method under the assumption of an observer at spatial infinity to obtain the waveform. For two cases in which the initial Gauss bump near the event horizon or at spatial infinity, we derive analytic expressions for the corresponding waveforms. Our results demonstrate that the waveform is indeed insensitive to tiny modifications of the effective potential, thereby confirming its stability. More importantly, we find that broader initial bumps imprint the influence of small environmental modifications more clearly on the waveform, which may provide theoretical guidance for probing the exterior environment of black holes. |
| title | Waveform stability for the piecewise step approximation of Regge-Wheeler potential |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2509.20947 |