On the dynamics of classicalization

We discuss the mechanism through which classicalization may occur during the collapse of a spherical field configuration modeled 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 waves. The full quantitative picture can be obtained only through the numerical integration of a partial differential equation of mixed type.