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Peer-reviewedCC BY 4.0Journal of High Energy Physics

Analyticity of the black hole S-matrix

  • Miguel Correia1
  • Tushar Gopalka2
  • Giulia Isabella2
  • Anna M. Wolz2
  1. 1McGill University
  2. 2Department of Physics and Astronomy, University of California Los Angeles
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Abstract

A bstract : 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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Cite

BibTeXRIS
BibTeX
@article{correia2026analyticity,
  title = {{Analyticity of the black hole S-matrix}},
  author = {Miguel Correia and Tushar Gopalka and Giulia Isabella and Anna M. Wolz},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = oct,
  doi = {10.1007/jhep10(2026)150},
  url = {https://link.springer.com/article/10.1007/JHEP10(2026)150},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Analyticity of the black hole S-matrix
AU  - Miguel Correia
AU  - Tushar Gopalka
AU  - Giulia Isabella
AU  - Anna M. Wolz
PY  - 2026
DA  - 2026/10/14
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep10(2026)150
UR  - https://link.springer.com/article/10.1007/JHEP10(2026)150
AB  - A bstract : 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.
SN  - 1029-8479
ER  -