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

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>ε</a:mi> </a:math> . It is found that for <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>ε</c:mi> <c:mo>&lt;</c:mo> <c:mn>1</c:mn> </c:math> all realized dust particle orbits are stable and for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>ε</e:mi> <e:mo>=</e:mo> <e:mn>1</e:mn> </e:math> all dust particles are in marginally stable states.