Dynamical Instability of Gaseous Sphere in the Reissner-Nordstrom Limit

TL;DR

This paper investigates the conditions under which gaseous spheres become dynamically unstable when approaching the Reissner-Nordström limit, deriving stability criteria and analyzing the effects of charge and relativistic regimes.

Contribution

It introduces a new linearized perturbation framework and stability criteria for charged gaseous spheres near the Reissner-Nordström limit, including both Newtonian and post-Newtonian regimes.

Findings

Dynamical instability occurs when the sphere contracts to the Reissner-Nordström radius.

Stability criteria depend on the adiabatic index and charge distribution.

Instability thresholds are characterized for homogeneous and polytropic spheres.

Abstract

In this paper, we study the dynamical instability of gaseous sphere under radial oscillations approaching the Reissner-Nordstr\"om limit. For this purpose, we derive linearized perturbed equation of motion following the Eulerian and Lagrangian approaches. We formulate perturbed pressure in terms of adiabatic index by employing the conservation of baryon numbers. A variational principle is established to evaluate characteristic frequencies of oscillations which lead to the criteria for dynamical stability. The dynamical instability of homogeneous sphere as well as relativistic polytropes with different values of charge in Newtonian and post-Newtonian regimes is explored. We also find their radii of instability in terms of the Reissner-Nordstrom radius. We conclude that dynamical instability occurs if the gaseous sphere contracts to the Reissner-Nordst\"orm radius for different values of charge.