Revised research about chaotic dynamics in Mankoet al.spacetime

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-Goméz, 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.

Adjusting chaotic indicators to curved spacetimes

“…4.1. By the means of this approximative technique, FLI has already been applied in a few works (see, e.g., [21,32]), but FLI has not yet been tested by applying the geodesic deviation technique according to the author's knowledge.…”

“…The fact that geodesic motion in MSM background exhibits chaotic behavior was shown in [31][32][33] mainly by studying Poincaré sections, but also by applying the FLI indicator [19] as defined in [16], and by the means of frequency analysis [33].…”

“…The numerical calculations were done in prolate spheroidal coordinates x, y, but the results are presented in cylindrical coordinates ρ, z to facilitate the comparison with previous works [31][32][33]. The two coordinate systems relate through the transformation…”

“…In these cases the indicators just have to verify the previous findings. Thus, the study starts with two cases of the MSM spacetime background, which were investigated in [32].…”

“…MSM background belongs to a broader family of spacetimes describing the surrounding spacetime of neutron stars; this family of spacetimes was introduced in [28] and revisited in [29], and their astrophysical importance was investigated in [29,30]. Now, from the dynamical point of view, since the existence of chaos in MSM background has already been revealed in [31][32][33], the MSM spacetime provides the appropriate background for testing chaotic indicators on geodesic orbits.…”