Unitarity alternatives in the reduced-action model for gravitational collapse

TL;DR

This paper analyzes the unitarity properties of a reduced-action model for gravitational collapse at transplanckian energies, confirming a critical impact parameter and exploring quantum transition contributions and string-scale regularizations.

Contribution

It provides a detailed analysis of unitarity in the reduced-action model, confirming the critical impact parameter and proposing alternative solutions involving string-scale effects.

Findings

Unitarity is maintained for impact parameters larger than b_c.

Exponential suppression of the S-matrix occurs for impact parameters smaller than b_c.

String-scale regularizations may recover lost probability.

Abstract

Based on the ACV approach to transplanckian energies, the reduced-action model for the gravitational S-matrix predicts a critical impact parameter b_c ~ R = 2 G sqrt{s} such that S-matrix unitarity is satisfied in the perturbative region b > b_c, while it is exponentially suppressed with respect to s in the region b < b_c that we think corresponds to gravitational collapse. Here we definitely confirm this statement by a detailed analysis of both the critical region b ~ b_c and of further possible contributions due to quantum transitions for b < b_c. We point out, however, that the subcritical unitarity suppression is basically due to the boundary condition which insures that the solutions of the model be ultraviolet-safe. As an alternative, relaxing such condition leads to solutions which carry short-distance singularities presumably regularized by the string. We suggest that through such solutions - depending on the detailed dynamics at the string scale - the lost probability may be recovered.