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arXiv · 2409.06681

Black hole scattering amplitudes via analytic small-frequency expansion and monodromy

Gleb Aminov·Paolo Arnaudo
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Abstract

We utilize three complementary approaches to pinpoint the exact form of scattering amplitudes in Schwarzschild spacetime. First, we solve the Regge-Wheeler equation perturbatively in the small-frequency regime. We use the obtained solutions to determine the monodromy in the near-spatial infinity region, which leads to a specific partial differential equation on the elements of the scattering matrix. As a result, it can be written in terms of the elements of the infinitesimal generator of the monodromy transformation and an integration constant. This constant is further related to the Nekrasov-Shatashvili free energy through the resummation of infinitely many instantons. The quasinormal mode frequencies are also studied in the small-frequency approximation.

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Gleb Aminov, Paolo Arnaudo. 2024-09-10. Black hole scattering amplitudes via analytic small-frequency expansion and monodromy. https://arxiv.org/abs/2409.06681

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