Quantum Tunneling and Unitarity Features of an S-matrix for Gravitational Collapse

TL;DR

This paper analyzes the S-matrix in gravitational collapse, revealing non-unitary behavior at certain impact parameters and proposing conditions under which unitarity can be restored, advancing understanding of quantum effects in gravity.

Contribution

It extends previous models to include inelastic processes, identifying conditions for unitarity restoration in quantum gravitational collapse scenarios.

Findings

Non-unitary S-matrix eigenvalues for impact parameters below critical value

Unitarity can be restored if the rapidity phase-space parameter exceeds a certain threshold

Provides a quantitative study of unitarity defect in quantum gravitational scattering

Abstract

Starting from the semiclassical reduced-action approach to transplanckian scattering by Amati, Veneziano and one of us and from our previous quantum extension of that model, we investigate the S-matrix expression for inelastic processes by extending to this case the tunneling features previously found in the region of classical gravitational collapse. The resulting model exhibits some non-unitary S-matrix eigenvalues for impact parameters b < b_c, a critical value of the order of the gravitational radius R = 2 G sqrt(s), thus showing that some (inelastic) unitarity defect is generally present, and can be studied quantitatively. We find that S-matrix unitarity for b < b_c is restored only if the rapidity phase-space parameter y is allowed to take values larger than the effective coupling G s / hbar itself. Some features of the resulting unitary model are discussed.