Green function of the Pöschl-Teller potential
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914531949674496 |
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| author | Kuntz, Adrien |
| author_facet | Kuntz, Adrien |
| contents | We use an approximation of the Regge-Wheeler-Zerilli potential, known as Pöschl-Teller, to exactly compute the time-domain Green function of black hole perturbations in this simplified model, taking into account all causality conditions. We find the existence of an additional early times piece in the Green function, contributing to new exponentially growing modes just before the signal interacts with the maximum of the potential. The waveform itself is decomposed as an instantaneous piece traveling exactly on the light-cones of the Green function and a historical piece depending on the past trajectory of the system inside the light-cone. We also study redshift modes and show that the Regge-Wheeler-Zerilli Green function is regular at their frequency, with no zero nor pole. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17954 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Green function of the Pöschl-Teller potential Kuntz, Adrien General Relativity and Quantum Cosmology High Energy Physics - Theory We use an approximation of the Regge-Wheeler-Zerilli potential, known as Pöschl-Teller, to exactly compute the time-domain Green function of black hole perturbations in this simplified model, taking into account all causality conditions. We find the existence of an additional early times piece in the Green function, contributing to new exponentially growing modes just before the signal interacts with the maximum of the potential. The waveform itself is decomposed as an instantaneous piece traveling exactly on the light-cones of the Green function and a historical piece depending on the past trajectory of the system inside the light-cone. We also study redshift modes and show that the Regge-Wheeler-Zerilli Green function is regular at their frequency, with no zero nor pole. |
| title | Green function of the Pöschl-Teller potential |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.17954 |