Exploring an S-matrix for gravitational collapse

TL;DR

This paper investigates an S-matrix approach to transplanckian scattering, demonstrating it captures key features of gravitational collapse, including singularities and critical scaling behaviors similar to classical collapse phenomena.

Contribution

It extends previous work by analyzing axisymmetric collisions without certain approximations, confirming the S-matrix's relevance to quantum gravitational collapse.

Findings

S-matrix develops singularities near collapse bounds

Location of singularities aligns with trapped-surface criteria

Elastic S-matrix phase shows universal fractional-power behavior

Abstract

We analyze further a recently proposed S-matrix description of transplanckian scattering in the specific case of axisymmetric collisions of extended sources, where some of the original approximations are not necessary. We confirm the claim that such an approximate description appears to capture the essential features of (the quantum counterpart of) classical gravitational collapse. More specifically, the S-matrix develops singularities whose location in the sources' parameter space are consistent with (and numerically close to) the bounds coming from closed-trapped-surface collapse criteria. In the vicinity of the critical "lines" the phase of the elastic S-matrix exhibits a universal fractional-power behaviour reminiscent of Choptuik's scaling near critical collapse.