High Energy Theory Seminar

The analytic structure of the black hole S-matrix encodes information about the response of a black hole to external perturbations and is required as input for S-matrix bootstrap applications. In this talk, I will describe how to define an IR-finite S-matrix for the classical scattering of a wave off a Schwarzschild black hole background. To understand its analytic structure, I will first present a proof of analyticity, unitarity, and reflection symmetry for wave scattering off generic backgrounds, based on properties of the background potential. I will then apply this result to the Schwarzschild black hole, deriving regions of analyticity for the S-matrix and validating them with both perturbative results from black hole perturbation theory and examples in exactly solvable regimes. I will show that the reflection amplitude of the S-matrix has a branch cut in the upper-half frequency plane that is consistent with causality, analyticity, unitarity, and reflection symmetry.

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