Three-dimensional general relativistic Poynting-Robertson effect. III. Static and non-spherical quadrupolar massive source

TL;DR

This paper explores the complex three-dimensional motion of particles around a non-spherical, quadrupolar massive object under relativistic radiation forces, revealing stable equilibrium regions and diverse orbital behaviors.

Contribution

It extends previous models by deriving equations of motion in a non-spherical, quadrupolar gravitational field with radiation effects, analyzing stability and orbit configurations.

Findings

Existence of a critical hypersurface where forces balance.

Stable configurations of particles on the hypersurface.

Multiple hypersurface solutions and orbital behaviors.

Abstract

We investigate the three-dimensional motion of a test particle in the gravitational field generated by a non-spherical compact object endowed with a mass quadrupole moment, described by the Erez-Rosen metric, and a radiation field, including the general relativistic Poynting-Robertson effect, coming from a rigidly rotating spherical emitting source located outside of the compact object. We derive the equations of motion for test particles influenced by such radiation field, recovering the two-dimensional description, and the weak-field approximation. This dynamical system admits the existence of a critical hypersurface, region where gravitational and radiation forces balance. Selected test particle orbits for different set of input parameters are displayed. The possible configurations on the critical hypersurfaces can be either latitudinal drift towards the equatorial ring or suspended orbits. We discuss about the existence of multiple hypersurface solutions through a simple method to perform the calculations. We graphically prove also that the critical hypersurfaces are stable configurations within the Lyapunov theory.