Gravitational and electric energies in the collapse of a spherical thin-shell capacitor

TL;DR

This paper analyzes how gravitational energy converts into kinetic and electric energies during the collapse of a spherical thin-shell capacitor, revealing energy distribution and microscopic electric effects influencing collapse dynamics.

Contribution

It provides an analytical model describing energy conversion and electric effects during spherical thin-shell capacitor collapse, highlighting the energy balance and microscopic electric processes.

Findings

Kinetic and electric energies are roughly equal during collapse.

Electric energy causes a sequence of 'on and off' energy exchange steps.

Collapse slows down due to electric energy rebuilding, extending collapse time.

Abstract

We adopt a simplified model describing the collapse of a spherical thin-shell capacitor to give an analytical description how gravitational energy is converted to both kinetic and electric energies in the gravitational collapse. It is shown that (i) averaged kinetic and electric energies are the same order, about an half of gravitational energy of spherical thin-shell capacitor in the collapse; (ii) caused by radiating and rebuilding electric energy, the gravitational collapse undergoes a sequence of "on and off" hopping steps in the microscopic Compton scale. Although the collapse process is still continuous in terms of macroscopic scales, it is slowed down as the kinetic energy is reduced and collapsing time is about an order of magnitude larger than that of the collapse process eliminating electric processes.