Black Hole Formation and Classicalization in Ultra-Planckian 2 -> N Scattering

TL;DR

This paper links ultra-Planckian scattering amplitudes to black hole formation, showing how microscopic graviton interactions explain black hole dominance and entropy through string theory and quantum criticality.

Contribution

It introduces a microscopic graviton-based model for black hole formation in high-energy scattering, connecting perturbative amplitudes with black hole entropy and the N-portrait.

Findings

Perturbative amplitudes match black hole entropy at critical N.

Exact solutions for scattering equations in the classicalization limit.

Demonstrates string and field theory complementarity in high-energy regimes.

Abstract

We establish a connection between the ultra-Planckian scattering amplitudes in field and string theory and unitarization by black hole formation in these scattering processes. Using as a guideline an explicit microscopic theory in which the black hole represents a bound-state of many soft gravitons at the quantum critical point, we were able to identify and compute a set of perturbative amplitudes relevant for black hole formation. These are the tree-level N-graviton scattering S-matrix elements in a kinematical regime (called classicalization limit) where the two incoming ultra-Planckian gravitons produce a large number N of soft gravitons. We compute these amplitudes by using the Kawai-Lewellen-Tye relations, as well as scattering equations and string theory techniques. We discover that this limit reveals the key features of the microscopic corpuscular black hole N-portrait. In particular, the perturbative suppression factor of a N-graviton final state, derived from the amplitude, matches the non-perturbative black hole entropy when N reaches the quantum criticality value, whereas final states with different value of N are either suppressed or excluded by non-perturbative corpuscular physics. Thus we identify the microscopic reason behind the black hole dominance over other final states including non-black hole classical object. In the parameterization of the classicalization limit the scattering equations can be solved exactly allowing us to obtain closed expressions for the high-energy limit of the open and closed superstring tree-level scattering amplitudes for a generic number N of external legs. We demonstrate matching and complementarity between the string theory and field theory in different large-s and large-N regimes.