Beyond quasinormal modes: a complete mode decomposition of black hole perturbations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914107543781376 |
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| author | Arnaudo, Paolo Carballo, Javier Withers, Benjamin |
| author_facet | Arnaudo, Paolo Carballo, Javier Withers, Benjamin |
| contents | We show that retarded Green's functions of black hole spacetimes can be expressed as a convergent mode sum everywhere in spacetime. At late times a quasinormal mode sum converges, while at early times a Matsubara (or, Euclidean) mode sum converges. The two regions are separated by a lightcone which scatters from the black hole potential. The Matsubara sum is a Fourier series on the Euclidean thermal circle associated to the early time region. We illustrate our results for Pöschl-Teller, BTZ, and Schwarzschild. In the case of Schwarzschild, we express the branch cut contribution as a convergent sum of de Sitter quasinormal modes as $Λ\to 0^+$, and exploit recent exact solutions to the Heun connection problem. In each case we analytically show convergence by studying the asymptotics of residue sums and also provide numerical demonstrations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Beyond quasinormal modes: a complete mode decomposition of black hole perturbations Arnaudo, Paolo Carballo, Javier Withers, Benjamin General Relativity and Quantum Cosmology High Energy Physics - Theory We show that retarded Green's functions of black hole spacetimes can be expressed as a convergent mode sum everywhere in spacetime. At late times a quasinormal mode sum converges, while at early times a Matsubara (or, Euclidean) mode sum converges. The two regions are separated by a lightcone which scatters from the black hole potential. The Matsubara sum is a Fourier series on the Euclidean thermal circle associated to the early time region. We illustrate our results for Pöschl-Teller, BTZ, and Schwarzschild. In the case of Schwarzschild, we express the branch cut contribution as a convergent sum of de Sitter quasinormal modes as $Λ\to 0^+$, and exploit recent exact solutions to the Heun connection problem. In each case we analytically show convergence by studying the asymptotics of residue sums and also provide numerical demonstrations. |
| title | Beyond quasinormal modes: a complete mode decomposition of black hole perturbations |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.18956 |