van Stockum--Bonnor Spacetimes of Rigidly Rotating Dust

Abstract

Stationary, axisymmetric and asymptotically flat spacetimes of dust of which trajectories are integral curves of the time translation Killing vector are investigated. The flow has no Newtonian limit. Asymptotic flatness implies the existence of singularities of the curvature scalar that are distributions and that are not isolated from regularity regions of the flow. The singularities are closely related to the presence of additional stresses that contribute negative active mass to the total (Komar) mass, which is zero for asymptotically flat spacetimes. Several families of solutions are constructed and a multipole expansion is presented.