Stability of neutral and charged Dyson shells around Reissner-Nordstrom compact objects

TL;DR

This paper demonstrates that neutral Dyson shells around charged Reissner-Nordstrom objects can be stable, with stability influenced by charge sign and electromagnetic interactions, contrasting with the instability of shells around uncharged objects.

Contribution

It analytically establishes stability conditions for charged Dyson shells in Reissner-Nordstrom spacetime, revealing the stabilizing effect of electromagnetic forces.

Findings

Neutral shells can be stable around charged objects.

Stability depends on the charge sign of the shell.

Oscillation frequency increases with shell mass.

Abstract

In this Letter, we show that, in contrast to Dyson shells surrounding uncharged compact objects, which are generally unstable, a neutral Dyson shell enclosing a charged compact object described by the Reissner-Nordstrom spacetime can attain a stable equilibrium configuration. We analytically derive the conditions for stability, determine the equilibrium radius and the corresponding minimum asymptotic energy, and show that small perturbations about this equilibrium lead to a stable oscillatory motion of the shell. The oscillation frequency is obtained explicitly and shown to increase with the shell mass and decrease with the charge of the central object. When the shell itself carries charge, its stability depends on the sign of this charge. Shells with the same sign as the central charge become progressively less stable, while oppositely charged shells exhibit enhanced stability due to the electrostatic attraction. These findings highlight the stabilizing role of electromagnetic interactions in Dyson-type thin-shell configurations within general relativity.