High-energy gravitational scattering and black hole resonances

TL;DR

This paper investigates high-energy gravitational scattering and black hole formation using partial-wave analysis, proposing a black hole ansatz for amplitudes that challenges traditional bounds but maintains causality.

Contribution

It introduces a novel black hole ansatz for scattering amplitudes that captures black hole formation features and explores their locality and causality properties.

Findings

Amplitudes deviate from Froissart bound and polynomial boundedness.

Black hole ansatz satisfies a macroscopic causality condition.

Partial-wave amplitudes derived for different impact parameter regimes.

Abstract

Aspects of super-planckian gravitational scattering and black hole formation are investigated, largely via a partial-wave representation. At large and decreasing impact parameters, amplitudes are expected to be governed by single graviton exchange, and then by eikonalized graviton exchange, for which partial-wave amplitudes are derived. In the near-Schwarzschild regime, perturbation theory fails. However, general features of gravitational scattering associated with black hole formation suggest a particular form for amplitudes, which we express as a black hole ansatz. We explore features of this ansatz, including its locality properties. These amplitudes satisfy neither the Froissart bound, nor apparently the more fundamental property of polynomial boundedness, through which locality is often encoded in an S-matrix framework. Nevertheless, these amplitudes do satisfy a macroscopic form of causality, expressed as a polynomial bound for the forward-scattering amplitude.