Circular geodesic orbits in the equatorial plane of a charged rotating disc of dust

Abstract: Equatorial circular geodesic orbits of neutral test particles in the exterior spacetime of a charged rotating disc of dust are analyzed in dependence of its specific charge and a relativity parameter. The charged rotating disc of dust is an axisymmetric, stationary solution of the Einstein-Maxwell equations in terms of a post-Newtonian expansion. In particular, photon, marginally bound and marginally stable orbits are discussed. It turns out that general formulae in closed form for angular velocity, specific energy and specific angular momentum of the test particles can be derived, which hold for any (exterior) asymptotically flat, axisymmetric, stationary and reflection symmetric (electro-)vacuum spacetime. Furthermore, circular motion in the exterior spacetime of the charged rotating disc of dust is qualitatively very similar to that around a Kerr-Newman black hole for sufficiently large radii, but differs strongly in the respective closer vicinity.