  We investigate the celestial description of an eikonal amplitude for the
scattering of massless scalars mediated by soft gravitons in the near-horizon
region of a large eternal Schwarzschild black hole. Our construction thus
provides a celestial conformal field theory on the horizon corresponding to a
non-perturbative scattering process that accounts for event horizons on
asymptotically flat spacetimes. From the \emph{known} two-dimensional
near-horizon scattering amplitude computed within the effective field theory
framework, we first construct a four-dimensional amplitude in a flat spacetime
frame around the bifurcation sphere strictly in a small angle approximation
limit. While the kinematics of external particles in this frame at leading
order are analogous to a Minkowski spacetime, the eikonal amplitude differs
from those about flat spacetime due to the near-horizon scattering potential.
We construct a celestial correlator following a Mellin transform that provides
an all loop order result, with a universal leading ultraviolet (UV) soft
scaling behavior of the conformally invariant cross-ratio, and an infrared (IR)
pole for the scaling dimension at each loop order. We argue these properties
manifest soft graviton exchanges in the near-horizon region and, consequently,
the soft UV behavior of the amplitude.
