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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.16054 |
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| _version_ | 1866917532647030784 |
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| author | Oltman, Izak Pineau, Ben |
| author_facet | Oltman, Izak Pineau, Ben |
| contents | This paper proposes a Poisson formula for the wave propagator of the Schwarzschild--de Sitter (SdS) metric. That is done by proving a Poisson formula relating wave propagators and scattering resonances for a class of non-compactly supported potentials on the real line. That class includes the Regge-Wheeler potentials obtained from separation of variables for SdS. The novelty lies in allowing non-compact supports -- all exact Poisson formulae of Lax-Phillips, Melrose, and other authors required compactness of the support of the perturbation. A key feature of the analysis is the presence of an exceptional class of potentials for which outgoing solutions may vanish at certain non-resonant frequencies. We identify and describe this class, which we call the resonant condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16054 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Poisson Formula for the Wave Propagator on Schwarzschild-de Sitter Backgrounds Oltman, Izak Pineau, Ben Analysis of PDEs This paper proposes a Poisson formula for the wave propagator of the Schwarzschild--de Sitter (SdS) metric. That is done by proving a Poisson formula relating wave propagators and scattering resonances for a class of non-compactly supported potentials on the real line. That class includes the Regge-Wheeler potentials obtained from separation of variables for SdS. The novelty lies in allowing non-compact supports -- all exact Poisson formulae of Lax-Phillips, Melrose, and other authors required compactness of the support of the perturbation. A key feature of the analysis is the presence of an exceptional class of potentials for which outgoing solutions may vanish at certain non-resonant frequencies. We identify and describe this class, which we call the resonant condition. |
| title | A Poisson Formula for the Wave Propagator on Schwarzschild-de Sitter Backgrounds |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.16054 |