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

TL;DR

The paper develops a bridge between perturbative graviton scattering amplitudes and non-perturbative black hole production by proposing a corpuscular, quantum-critical picture of black holes. It analyzes 2 → N graviton processes in the classicalization regime, employing field-theory KLT relations and string theory formalisms, and uses scattering equations to obtain exact large-N results. A key finding is that perturbative suppression of 2 → N amplitudes is precisely compensated by the exponential degeneracy of black hole microstates at the quantum critical point, explaining BH dominance over other macroscopic final states. The work also demonstrates consistent field/string theory descriptions in large-s regimes and uncovers structural links to Jacobi-polynomial solutions of the scattering equations, offering insights into how unitarization by BH formation emerges from perturbative graviton dynamics.

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.

Figures (7)

• Figure 1: Bose--Einstein levels and black hole formation.
• Figure 2: Graviton physics and interplay between field and string theory as variation of $\lambda$.
• Figure 3: Perturbative and non-perturbative regimes as variation of $\lambda$.
• Figure 4: Tree level scattering of $2$ into $N-2$ particles. The blob can be thought of as the sum over all Feynman diagrams at tree level.
• Figure 5: Production of a black hole and decay into $N-2$ soft quanta each with momenta $\sim \frac{\sqrt{s}}{N-2}$. The circle with the wiggly double lines depicts the Bose-Einstein condensate nature of the black hole.