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arXiv · 2310.03430

Celestial Eikonal Amplitudes in the Near-Horizon Region

Karan Fernandes·Feng-Li Lin·Arpita Mitra
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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.

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Karan Fernandes, Feng-Li Lin, Arpita Mitra. 2023-10-05. Celestial Eikonal Amplitudes in the Near-Horizon Region. https://doi.org/10.1103/physrevd.110.126011

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