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

TL;DR

This paper analyzes equatorial circular geodesic orbits around a charged rotating disc of dust, deriving general formulas and comparing the orbital dynamics to those around Kerr-Newman black holes, highlighting similarities at large radii and differences closer in.

Contribution

It provides closed-form expressions for test particle orbits in the exterior spacetime of a charged rotating dust disc, extending understanding of axisymmetric solutions in Einstein-Maxwell theory.

Findings

Orbital properties depend on the disc's charge and relativity parameter.

Close to the disc, orbital behavior differs significantly from black hole spacetimes.

At large distances, orbits resemble those around Kerr-Newman black holes.

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.