Orbital dynamics and spin-precession around a circular chiral vorton

TL;DR

This work analyzes the motion of massive and massless test particles and gyroscope spin in the weak-field spacetime of a circular chiral vorton, deriving reduced geodesic equations to order $\mathcal{O}(G\mu)$ and computing both geodetic and Lense–Thirring precession frequencies. It reveals a rich dynamical landscape, including equatorial precession, toroidal and crown-like bound orbits, and diverse unbound/null trajectories, with a clear signature of frame dragging and non-separability leading to potential chaos as shown by PSOS analyses. The study also develops general spin-precession formalisms for stationary observers, uncovering distinctive precession patterns (e.g., two-minima structures) that differ from Kerr black holes and share some features with Kerr naked singularities, especially near the ring core and ergoregion. The results point to observational avenues, such as pulsar timing and gravitational lensing, for probing vortons, while highlighting that extending beyond the weak-field approximation is essential for robust strong-field predictions.

Abstract

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.

Figures (22)

• Figure 1: Radial profile of $V_{\text{eff}}(r)$ for several values of the angular momentum $L$.
• Figure 2: The landscape of effective potential surface $V_{\text{eff}}(r,z)$, showing the bound region for test-particle motion for $G\mu = 0.0001$ and $L=0.0001$.
• Figure 3: Precessing timelike orbits around a chiral vorton (red) with counter-clockwise frame dragging (blue arrow): (a) prograde and (b) retrograde initial angular velocities.
• Figure 4: Bound precessing-ellipse trajectories of a massive test particle ($\epsilon = -1$). A circular orbit is shown for comparison in panel (f).
• Figure 5: Toroidal orbits of a massive particle around a vorton. Initial velocity is applied along the $z$-axis for a particle starting in the $xy$ plane. each column corresponds to a single orbits: top row – 3D view; middle row – top-down view in the $xy$ plane; bottom row – radial and vertical ($r$–$z$) trajectory, with the particle’s trajectory around the vorton superimposed.