Celestial eikonal amplitudes in the near-horizon region

We construct a celestial conformal field theory on the horizon corresponding to a nonperturbative eikonal scattering amplitude involving two massless scalars mediated by soft gravitons in the near-horizon region of a large eternal Schwarzschild black hole. From the known two-dimensional near-horizon scattering amplitude computed within the effective field theory framework, we first construct a four-dimensional amplitude involving two external s-wave legs in a flat spacetime frame around the bifurcation sphere strictly in a small angle approximation limit by resumming over the spherical harmonics. 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 derive a celestial correlator following a Mellin transform that provides an all loop order result, with a universal leading UV soft scaling behavior of the conformally invariant cross-ratio, and an 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.