Scalar field scattering in a Schwarzschild-de Sitter geometry
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917076179877888 |
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| author | de Cesare, Marco Miranda, Marcello Porfyriadis, Achilleas P. |
| author_facet | de Cesare, Marco Miranda, Marcello Porfyriadis, Achilleas P. |
| contents | We solve analytically the low-frequency s-wave dynamics of a massless scalar field propagating on a Schwarzschild-de Sitter black hole background. A rigorous application of the method of matched asymptotic expansions allows us to connect the scalar's evolution in the proximity of the black-hole horizon with that on cosmological scales. The scattering coefficients, greybody factors, and Wigner time delay are computed explicitly. We consider both small and large black holes, with black-hole to cosmological horizon radii parametrically small and of order unity, respectively. This extends previous studies confined to the small black-hole regime only. In addition, for small black holes we perform a calculation that remains agnostic about the relative size between the ratio of the geometry's horizons and the scalar's frequency in units of the black-hole radius. When the two are comparable, we find that they are interchangeable in the greybody factor, which is symmetric under $ω\leftrightarrow 1/r_c$ (where $ω$ is the scalar's frequency and $r_c$ the cosmological horizon radius). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scalar field scattering in a Schwarzschild-de Sitter geometry de Cesare, Marco Miranda, Marcello Porfyriadis, Achilleas P. General Relativity and Quantum Cosmology High Energy Physics - Theory We solve analytically the low-frequency s-wave dynamics of a massless scalar field propagating on a Schwarzschild-de Sitter black hole background. A rigorous application of the method of matched asymptotic expansions allows us to connect the scalar's evolution in the proximity of the black-hole horizon with that on cosmological scales. The scattering coefficients, greybody factors, and Wigner time delay are computed explicitly. We consider both small and large black holes, with black-hole to cosmological horizon radii parametrically small and of order unity, respectively. This extends previous studies confined to the small black-hole regime only. In addition, for small black holes we perform a calculation that remains agnostic about the relative size between the ratio of the geometry's horizons and the scalar's frequency in units of the black-hole radius. When the two are comparable, we find that they are interchangeable in the greybody factor, which is symmetric under $ω\leftrightarrow 1/r_c$ (where $ω$ is the scalar's frequency and $r_c$ the cosmological horizon radius). |
| title | Scalar field scattering in a Schwarzschild-de Sitter geometry |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.09168 |