  We describe a unitary scattering process, as observed from spatial infinity,
of massless scalar particles on an asymptotically flat Schwarzschild black hole
background. In order to do so, we split the problem in two different regimes
governing the dynamics of the scattering process. The first describes the
evolution of the modes in the region away from the horizon and can be analysed
in terms of the effective Regge-Wheeler potential. In the near horizon region,
where the Regge-Wheeler potential becomes insignificant, the WKB geometric
optics approximation of Hawking's is replaced by the near-horizon gravitational
scattering matrix that captures non-perturbative soft graviton exchanges near
the horizon. We perform an appropriate matching for the scattering solutions of
these two dynamical problems and compute the resulting Bogoliubov relations,
that combines both dynamics. This allows us to formulate an S-matrix for the
scattering process that is manifestly unitary. We discuss the analogue of the
(quasi)-normal modes in this setup and the emergence of gravitational echoes
that follow an original burst of radiation as the excited black hole relaxes to
equilibrium.
