Analyticity of the Black Hole S-Matrix
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911289331154944 |
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| author | Correia, Miguel Gopalka, Tushar Isabella, Giulia Wolz, Anna M. |
| author_facet | Correia, Miguel Gopalka, Tushar Isabella, Giulia Wolz, Anna M. |
| contents | We establish the analytic structure of the S-matrix in the complex-frequency plane for classical wave scattering on a Schwarzschild background in four space-time dimensions. Our argument relies on the analytic continuation of the gravitational potential, with the singularity behind the horizon playing a crucial role. We find that in the lower half-plane the partial-wave amplitudes are analytic except for the quasinormal-mode poles and the branch cut associated with late-time tails. As a direct consequence of causality, the retarded Green's function and absorption amplitude are analytic in the upper-half plane. We show, however, that Stokes phenomena can obstruct this analyticity domain from carrying over to the elastic amplitude, which instead develops a branch-cut in the upper-half plane. We also determine the effect of infrared (IR) regulators on the analytic structure, showing that polynomial boundedness requires a sharp lower bound on the IR cutoff in terms of the Schwarzschild radius. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11794 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analyticity of the Black Hole S-Matrix Correia, Miguel Gopalka, Tushar Isabella, Giulia Wolz, Anna M. High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics We establish the analytic structure of the S-matrix in the complex-frequency plane for classical wave scattering on a Schwarzschild background in four space-time dimensions. Our argument relies on the analytic continuation of the gravitational potential, with the singularity behind the horizon playing a crucial role. We find that in the lower half-plane the partial-wave amplitudes are analytic except for the quasinormal-mode poles and the branch cut associated with late-time tails. As a direct consequence of causality, the retarded Green's function and absorption amplitude are analytic in the upper-half plane. We show, however, that Stokes phenomena can obstruct this analyticity domain from carrying over to the elastic amplitude, which instead develops a branch-cut in the upper-half plane. We also determine the effect of infrared (IR) regulators on the analytic structure, showing that polynomial boundedness requires a sharp lower bound on the IR cutoff in terms of the Schwarzschild radius. |
| title | Analyticity of the Black Hole S-Matrix |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2511.11794 |