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arXiv · 2511.09168

Scalar field scattering in a Schwarzschild-de Sitter geometry

Marco de Cesare·Marcello Miranda·Achilleas P. Porfyriadis
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Abstract

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 $\omega\leftrightarrow 1/r_c$ (where $\omega$ is the scalar's frequency and $r_c$ the cosmological horizon radius).

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Marco de Cesare, Marcello Miranda, Achilleas P. Porfyriadis. 2025-11-12. Scalar field scattering in a Schwarzschild-de Sitter geometry. https://arxiv.org/abs/2511.09168

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