Celestial Eikonal Amplitudes in the Near-Horizon Region

TL;DR

This paper develops a celestial conformal field theory description of near-horizon scattering amplitudes involving soft gravitons around a Schwarzschild black hole, revealing universal soft behaviors and IR poles at all loop orders.

Contribution

It constructs a non-perturbative celestial amplitude for near-horizon scattering, extending the celestial holography framework to black hole horizons with loop-level results.

Findings

Universal UV soft scaling behavior identified

Infrared pole at each loop order in the conformal cross-ratio

All loop order celestial correlator constructed

Abstract

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.