Revised research about chaotic dynamics in Manko et al. spacetime

TL;DR

This study re-evaluates chaos in test particle motion around rotating neutron stars described by Manko et al., finding chaos occurs only with prolate deformation, contrary to previous claims of oblate deformation causing chaos.

Contribution

It clarifies the conditions for chaos in Manko et al. spacetime, showing chaos occurs with prolate deformation and correcting prior misconceptions about oblate deformation.

Findings

Chaos occurs only with prolate deformation.

Chaos is outside the stars with large mass-quadrupole moments.

Orbits are regular for oblate deformation, consistent with real star shapes.

Abstract

A recent work by Dubeibe et al. [Phys. Rev. D 75, 023008 (2007)] stated that chaos phenomenon of test particles in gravitational field of rotating neutron stars which are described by Manko, Sanabria-Gomez, and Manko (Manko et al.) metric can only occur when the stars have oblate deformation. But the chaotic motions they found are limited in a very narrow zone which is very close to the center of the massive bodies. This paper argues that this is impossible because the region is actually inside of the stars, so the motions cannot exist at this place. In this paper, we scan all parameters space and find chaos and unstable fixed points outside of stars with big mass-quadrupole moments. The calculations show that chaos can only occur when the stars have prolate deformation. Because real deformation of stars should be oblate, all orbits of test particles around the rotating neutron stars described by Manko et al. solutions are regular. The case of nonzero dipolar magnetic moment has also been taken into account in this study.