Classical dynamics and stability of collapsing thick shells of matter

TL;DR

This paper analyzes the classical dynamics and stability of collapsing thick shells of matter with electric charge and cosmological constant, using Israel's junction conditions and a mean field approach, with brief comments on quantum effects.

Contribution

It introduces a detailed classical model for the collapse of charged thick shells, incorporating stability analysis and potential quantum extensions.

Findings

Derived an effective Hamiltonian for microshell motion.

Assessed stability conditions of the macroshell.

Discussed possible quantum effects in collapse scenarios.

Abstract

We study the collapse towards the gravitational radius of a macroscopic spherical thick shell surrounding an inner massive core. This overall electrically neutral macroshell is composed by many nested delta-like massive microshells which can bear non-zero electric charge, and a possibly non-zero cosmological constant is also included. The dynamics of the shells is described by means of Israel's (Lanczos) junction conditions for singular hypersurfaces and, adopting a Hartree (mean field) approach, an effective Hamiltonian for the motion of each microshell is derived which allows to check the stability of the matter composing the macroshell. We end by briefly commenting on the quantum effects which may arise from the extension of our classical treatment to the semiclassical level.