Towards an S-matrix Description of Gravitational Collapse

TL;DR

This paper investigates the behavior of the S-matrix in high-energy gravitational scattering, revealing a divergence at a critical impact parameter and suggesting a quantum tunneling process near black-hole formation.

Contribution

It extends previous work by calculating the S-matrix at small impact parameters and identifying a divergence indicating a transition to a new regime related to gravitational collapse.

Findings

Perturbative expansion diverges at a critical impact parameter.

The S-matrix becomes absorptive and complex-valued below this critical impact parameter.

Field solutions remain regular, indicating quantum tunneling rather than classical singularity.

Abstract

Extending our previous results on trans-Planckian ($Gs \gg \hbar$) scattering of light particles in quantum string-gravity we present a calculation of the corresponding S-matrix from the region of large impact parameters ($b \gg G\sqrt{s}>\lambda_s$) down to the regime where classical gravitational collapse is expected to occur. By solving the semiclassical equations of a previously introduced effective-action approximation, we find that the perturbative expansion around the leading eikonal result diverges at a critical value $b = b_c = O(G\sqrt{s})$, signalling the onset of a new (black-hole related?) regime. We then discuss the main features of our explicitly unitary S-matrix -- and of the associated effective metric -- down to (and in the vicinity of) $b = b_c$, and present some ideas and results on its extension all the way to the $ b \to 0$ region. We find that for $b<b_c$ the physical field solutions are complex-valued and the S-matrix shows additional absorption, related to a new production mechanism. The field solutions themselves are, surprisingly, everywhere regular, suggesting a quantum-tunneling -- rather than a singular-geometry -- situation.