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arXiv · 2511.11794

Analyticity of the Black Hole S-Matrix

Miguel Correia·Tushar Gopalka·Giulia Isabella·Anna M. Wolz
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Abstract

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.

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Miguel Correia, Tushar Gopalka, Giulia Isabella, Anna M. Wolz. 2025-11-14. Analyticity of the Black Hole S-Matrix. https://arxiv.org/abs/2511.11794

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