Equatorial stability analysis of dust particle orbits within a charged rotating disc of dust

TL;DR

This paper analyzes the stability of dust particle orbits within a charged, rotating disc of dust using Einstein-Maxwell theory, revealing stability conditions based on the specific charge parameter.

Contribution

It provides a stability analysis of dust particle orbits in a charged rotating disc within Einstein-Maxwell theory, highlighting the role of the specific charge in orbital stability.

Findings

For psilon<1, all dust particle orbits are stable.

At psilon=1, dust particles are marginally stable.

The analysis is based on a post-Newtonian expansion of the axisymmetric solution.

Abstract

Stability of circular orbits of the dust particles within a charged rotating disc of dust with respect to perturbations in the equatorial plane is analyzed. Within Einstein-Maxwell theory, the charged rotating disc of dust is an axisymmetric, stationary solution given in terms of a post-Newtonian expansion. The disc solution is characterized by a rigid rotation around the axis of symmetry and a constant specific charge $\epsilon$. It is found that for $\epsilon<1$ all realized dust particle orbits are stable and for $\epsilon=1$ all dust particles are in marginally stable states.