On the dynamics of classicalization

TL;DR

This paper explores the classicalization process during spherical field collapse, showing it involves a transition from hyperbolic to elliptic equations, wave propagation cessation, and shock formation, with numerical methods needed for full understanding.

Contribution

It demonstrates the dynamical change in the equation type during classicalization and rederives the classicalization radius, providing new insights into the phenomenon.

Findings

Classicalization involves a transition from hyperbolic to elliptic PDEs.

Wave propagation is suppressed below the classicalization radius.

Shock fronts are generated during the process.

Abstract

We discuss the mechanism through which classicalization may occur during the collapse of a spherical field configuration modelled as a wavepacket. We demonstrate that the phenomenon is associated with the dynamical change of the equation of motion from a second-order partial differential equation of hyperbolic to one of elliptic type. Within this approach, we rederive the known expression for the classicalization radius. We also find indications that classicalization is associated with the absence of wave propagation at distances below the classicalization radius and the generation of shock fronts. The full quantitative picture can be obtained only through the numerical integration of a partial differential equation of mixed type.