Description
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
scattering of a classical 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 of 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.