Particle motion in a rotating dust spacetime: the Bonnor solution

TL;DR

This paper analyzes the Bonnor spacetime, a rotating dust solution with a singularity and closed timelike curves, exploring geodesic behavior, causal structure, and potential mechanisms to prevent particles from entering causality-violating regions.

Contribution

It provides a detailed classification of geodesic orbits and investigates the effects of friction forces on particle motion in Bonnor's spacetime, highlighting new insights into causality violations.

Findings

Test particles with positive angular momentum are repelled from the CTC boundary.

Particles with negative angular momentum can enter the pathological region under certain conditions.

Friction forces may prevent particles from approaching the CTC region.

Abstract

We investigate the geometrical properties, spectral classification, geodesics, and causal structure of the Bonnor's spacetime [Journal of Physics A Math. Gen., \textbf{10}, 1673 (1977)], i.e., a stationary axisymmetric solution with a rotating dust as a source. This spacetime has a directional singularity at the origin of the coordinates (related to the diverging vorticity field of the fluid there), which is surrounded by a toroidal region where closed timelike curves (CTCs) are allowed, leading to chronology violations. We use the effective potential approach to provide a classification of the different kind of geodesic orbits on the symmetry plane as well as to study the helical-like motion aroud the symmetry axis on a cylinder with constant radius. In the former case we find that as a general feature for positive values of the angular momentum test particles released from a fixed space point and directed towards the singularity are repelled and scattered back as soon as they approach the CTC boundary, without reaching the central singularity. In contrast, for negative values of the angular momentum there exist conditions in the parameter space for which particles are allowed to enter the pathological region. Finally, as a more realistic mechanism, we study accelerated orbits undergoing friction forces due to the interaction with the background fluid, which may also act in order to prevent particles from approaching the CTC region.