Dynamics of a thin shell in the Reissner-Nordstrom metric

TL;DR

This paper analyzes the dynamics of a thin, spherically symmetric, electrically neutral shell in the Reissner-Nordstrom black hole spacetime, revealing conditions for stable oscillations and constructing global geometric diagrams.

Contribution

It provides an analytical description of shell motion in charged black hole spacetime and demonstrates the possibility of stable oscillations for various equations of state.

Findings

Stable oscillating shell motions are possible under certain initial conditions.

Constructed Carter-Penrose diagrams illustrating all solution types.

Oscillations occur for arbitrary polytropic equations of state.

Abstract

We describe the dynamics of a thin spherically symmetric gravitating shell in the Reissner-Nordstrom metric of the electrically charged black hole. The energy-momentum tensor of electrically neutral shell is modelled by the perfect fluid with a polytropic equation of state. The motion of a shell is described fully analytically in the particular case of the dust equation of state. We construct the Carter-Penrose diagrams for the global geometry of the eternal black hole, which illustrate all possible types of solutions for moving shell. It is shown that for some specific range of initial parameters there are possible the stable oscillating motion of the shell transferring it consecutively in infinite series of internal universes. We demonstrate also that this oscillating type of motion is possible for an arbitrary polytropic equation of state on the shell.