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

TL;DR

This work analyzes the stability of Dyson-type thin shells surrounding a charged compact object in Einstein-Maxwell theory. It applies the Israel junction conditions and an asymptotic-energy minimization approach to derive a stable equilibrium radius $R_{ ext{eq}}$ and a corresponding minimum energy $E_{0,\min}$ for a neutral shell, with a closed-form expression for the oscillation frequency $\omega$ around equilibrium. The study shows that central charge stabilizes a neutral shell, and that shell charge $q$ can either destabilize (same sign) or stabilize (opposite sign) the configuration, depending on the parameter regime. These results reveal electromagnetic stabilization as a natural mechanism for Dyson-type thin-shell configurations and discuss the local, fixed-background limitations relevant to cosmic censorship and RN overcharged spacetimes.

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.

Figures (5)

• Figure 1: The asymptotic energy $E_{0}$ of Eq. (\ref{['11']}) as a function of $R_{0}$ for $M=1.0$, $Q=2.0$, and $m$ ranging from $0.00$ (bottom) to $0.50$ (top) in equal intervals. The minimum energy $E_{0}(\mathrm{min})$ corresponds to the stable configuration of the Dyson shell. Remarkably, the shell remains dynamically stable even in the absence of any shell charge.
• Figure 2: The effective potential $V_{\mathrm{eff}}$ of the one-dimensional motion of the Dyson shell versus $x=R/M$ for $q=2$ and $\mu=0.10$ (bottom) to $0.50$ (top) in equal intervals. The minimum potential corresponds to the stable equilibrium radius depicted in Fig. \ref{['F1']}. Remarkably, the shell remains dynamically stable even in the absence of any shell charge.
• Figure 3: The oscillation frequency $\omega$ of the Dyson shell under small perturbations around the stable equilibrium radius $R=R_{\mathrm{eq}}$, plotted versus $\mu$ for $q=1.20$ (top) to $3.20$ (bottom) in equal intervals. Increasing the shell mass (with fixed $M$ and $Q$) increases the frequency, indicating stronger stability, while increasing the charge of the central object (with fixed $M$ and $m$) reduces it. Remarkably, the shell remains dynamically stable even in the absence of any shell charge.
• Figure 4: The asymptotic energy $E_{0}$ of the charged Dyson shell as a function of $R_{0}$ for fixed values $M=1.0$, $Q=2.0$, and $m=0.50$, and for various shell charges $q$ ranging from $0.00$ (bottom) to $0.25$ (top). As seen, while the neutral Dyson shell is strongly stable, adding charge to the shell first weakens its stability and eventually renders it unstable.
• Figure 5: The asymptotic energy $E_{0}$ of the charged Dyson shell as a function of $R_{0}$ for fixed values $M=1.0$, $Q=2.0$, and $m=0.50$, and for various shell charges $q$ ranging from $-0.25$ (bottom) to $0.00$ (top). The opposite signs of charge between the central compact object and the shell enhance the stability of the Dyson shell.