Orbital dynamics and spin-precession around a circular chiral vorton

Vortons are of interest in high-energy physics as possible dark matter candidates and as probes of Grand Unified Theories. Using the recently derived weak-field metric for a chiral vorton, we study the dynamics of test particles by analyzing both timelike and null geodesics. We identify several classes of trajectories, including bound precessing orbits, circular orbits, toroidal, and crown-type oscillations, as well as unbound scattering paths. Poincare surfaces of section reveal transitions between regular and chaotic motions that depend sensitively on the vorton tension $Gμ$ and initial conditions. We further compute the Lense-Thirring and general spin-precession frequencies for gyroscopes along Killing trajectories. The resulting precession profiles exhibit several distinct features not present in Kerr black holes but reminiscent of Kerr naked singularities, such as: divergences near the ring core, and multi-minima structures. These dynamical and precessional signatures may offer potential observational pathways for detecting vortons.

💡 Research Summary

This paper presents a comprehensive study of particle and photon motion, as well as gyroscope spin‑precession, in the weak‑field spacetime generated by a circular chiral vorton – a hypothetical superconducting cosmic‑string loop that carries a persistent current and thus possesses intrinsic angular momentum. Starting from the metric derived in a previous work (first‑order in the string tension (G\mu)), the authors write the line element in cylindrical coordinates with two Killing vectors (\partial_t) and (\partial_\phi). The gravitational potential (\nu(r,z)) and the frame‑dragging potential (A(r,z)) are expressed through complete elliptic integrals (K) and (E). Both functions diverge at the string core ((r=R,,z=0)), a feature of the thin‑string approximation that can be regularized by introducing a finite core radius.

Using the geodesic Lagrangian (L=g_{\mu\nu}\dot x^\mu\dot x^\nu=\epsilon) ((\epsilon=-1) for massive particles, (\epsilon=0) for photons), the authors eliminate (\dot t) and (\dot\phi) in favor of the conserved energy (E) and angular momentum (L). To first order in (G\mu) the equations of motion reduce to a set of three coupled second‑order equations for (r(\tau)), (z(\tau)) and (\phi(\tau)). The radial dynamics can be encoded in an effective potential \