SciPost Submission Page
Green function of the Poschl-Teller potential
by Adrien Kuntz
Submission summary
| Authors (as registered SciPost users): | Adrien Kuntz |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202510_00057v1 (pdf) |
| Date submitted: | Oct. 29, 2025, 7:12 p.m. |
| Submitted by: | Adrien Kuntz |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We use an approximation of the Regge-Wheeler-Zerilli potential, known as Poschl-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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block