Stable attractors in the three-dimensional general relativistic Poynting-Robertson effect

TL;DR

This paper proves the stability of critical hypersurfaces in the three-dimensional general relativistic Poynting-Robertson effect, showing the equatorial ring as a stable attractor using a new Lyapunov-based approach.

Contribution

It introduces a simpler, more physical Lyapunov method and three different Lyapunov functions to analyze stability in this relativistic dynamical system.

Findings

Equatorial ring is a stable attractor.

Critical hypersurfaces form a basin of attraction.

New Lyapunov approach simplifies stability analysis.

Abstract

We prove the stability of the critical hypersurfaces associated with the three-dimensional general relativistic Poynting-Robertson effect. The equatorial ring configures to be as a stable attractor and the whole critical hypersurface as a basin of attraction for this dynamical system. We introduce a new, simpler (in terms of calculations), and more physical approach within the Lyapunov theory. We propose three different Lyapunov functions, each one carrying important information and very useful for understanding such phenomenon under different aspects.